Arsenal took full advantage of an uncertain performance from an injury-hit Hammers side playing in an almost funereal atmosphere at a normally boisterous ground, after a day that seemed set to be Grant's last stand.
The Gunners gave a fluent and assured display as they moved within one point of Manchester United and stayed three behind Premier League leaders Manchester City, although Arsene Wenger's side rarely needed to be at their best against such troubled opponents.
The visitors had endured a torrid week of their own, drawing at home to Leeds in the FA Cup and losing to Ipswich in the Carling Cup, but they took the lead with the first meaningful attack of the game after a lapse by Bridge, who endured a disastrous Hammers debut.
The left-back, who joined the club this week on a reportedly extravagant salary despite only starting one league match this season for Manchester City, was exposed for all three of Arsenal's goals.
Under-pressure Grant salutes fans
For the first, the 30-year-old allowed Walcott space on the right to send in a pass that was expertly dummied by Samir Nasri, allowing Van Persie to swivel and smash right-footed past Robert Green.
Walcott should have doubled the Gunners' lead after wriggling free of James Tomkins on the break but the winger hit a weak shot straight at Green.
The depleted Hammers, who were without the injured Scott Parker and lost Mark Noble early in the game, were offered mild encouragement by a nervy start from the Gunners' inexperienced backline, with a mistake from Johan Djourou almost leading to a Hammers equaliser.
The centre-back's sloppy backpass let Cole through on goal but Szczesny parried superbly and Zavon Hines blazed a follow-up chance over the bar.
It looked a costly miss because at the other end it seemed the slick Gunners could score at will.
Nasri should have done better with an effort that went straight at Green and Van Persie hammered a shot against the post from 12 yards.
But the visitors did not have to wait much longer for their second goal as Van Persie, played onside by Bridge, burst to the byline and pulled the ball back for Walcott to blast into the roof of the net from six yards.
Wenger sympathises with Grant
The Hammers had an instant chance to reply but Cole sent a header off target after being set up by an excellent Freddie Sears cross.
A relaxed Arsenal continued to control the game after the break and peppered the Hammers goal, although the hosts almost grabbed a fortuitous lifeline when Sears' miss-hit cross was tipped just wide by Szczesny.
The last flickers of a Hammers challenge, and perhaps of Grant's reign at the club, were extinguished when the hapless Bridge hacked down Walcott in the box and Van Persie stepped up to fire confidently into the bottom corner.
West Ham had the excellent Green to thank for keeping the score respectable, the keeper parrying a late Jack Wilshere effort just wide at a rapidly emptying stadium.
There were just about enough spectators remaining to give Grant a subdued send-off at the final whistle, the ever-dignified manager applauding the fans and slinging a claret and blue scarf - which just days ago he had dubbed his "lucky" garment - into the crowd.
Arsenal manager Arsene Wenger: "We had a good, mature performance today. It became pretty comprehensive.
"I said many times that the Premier League will be exciting and interesting until the end.
"It is in our hands, we play all of the big teams at home and we have a strong run at home now."
90:00+3:01 The referee signals the end of the game.
89:04 Short corner taken by Robin van Persie.
88:47 Jack Wilshere takes a shot. Robert Green makes a save.
88:37 Short corner taken by Robin van Persie from the left by-line.
88:13 Substitution Frank Nouble on for Wayne Bridge.
87:03 Substitution Kieran Gibbs joins the action as a substitute, replacing Theo Walcott.
87:03 Substitution Andrey Arshavin is brought on as a substitute for Samir Nasri.
86:34 Samir Nasri takes a shot. Matthew Upson gets a block in.
80:09 Carlton Cole is ruled offside. Wojciech Szczesny restarts play with the free kick.
80:09 Substitution Neves Denilson is brought on as a substitute for Francesc Fabregas.
78:59 Free kick awarded for an unfair challenge on Zavon Hines by Emmanuel Eboue. The free kick is delivered right-footed by Julien
Faubert from left wing, Johan Djourou manages to make a clearance.
77:06 Johan Djourou gives away a free kick for an unfair challenge on Luis Boa Morte. Direct free kick taken by Wayne Bridge.
76:11 Theo Walcott fouled by Wayne Bridge, the ref awards a Penalty.
76:11 GOAL - Robin van Persie:West Ham 0 - 3 Arsenal Robin van Persie scores a penalty. West Ham 0-3 Arsenal.
73:57 Jonathan Spector challenges Laurent Koscielny unfairly and gives away a free kick. Free kick taken by Gael Clichy.
68:06 Close range headed effort by Theo Walcott misses to the right of the goal.
66:26 Corner from the left by-line taken by Samir Nasri, clearance by James Tomkins.
63:55 Carlton Cole fouled by Gael Clichy, the ref awards a free kick. Direct free kick taken by Julien Faubert.
63:20 Substitution Pablo Barrera on for Freddie Sears.
62:35 The assistant referee flags for offside against Zavon Hines. Emmanuel Eboue restarts play with the free kick.
61:08 Corner taken by Wayne Bridge, Laurent Koscielny manages to make a clearance.
Correction - 60:45 Freddie Sears takes a shot. Wojciech Szczesny makes a save.
60:45 Jack Wilshere takes a shot. Save by Wojciech Szczesny.
59:47 The referee blows for offside against Samir Nasri. Free kick taken by Robert Green.
59:13 Corner taken short by Francesc Fabregas.
57:59 Luis Boa Morte challenges Jack Wilshere unfairly and gives away a free kick. Shot on goal comes in from Robin van Persie from
the free kick, blocked by Matthew Upson.
56:33 Unfair challenge on Luis Boa Morte by Robin van Persie results in a free kick. Luis Boa Morte restarts play with the free
kick.
55:33 The referee gives a free kick against Samir Nasri for handball. Robert Green takes the free kick.
54:24 Theo Walcott takes a shot. Save by Robert Green.
51:54 Corner taken by Wayne Bridge from the right by-line, Jack Wilshere makes a clearance.
50:41 Foul by Laurent Koscielny on Jonathan Spector, free kick awarded. Wayne Bridge produces a strike on goal direct from the free
kick.
49:41 Shot from just outside the box by Robin van Persie goes over the bar.
48:50 Robin van Persie decides to take the corner short.
48:31 Zavon Hines gives away a free kick for an unfair challenge on Emmanuel Eboue. Emmanuel Eboue takes the direct free kick.
47:43 Theo Walcott produces a right-footed shot from just outside the penalty box that misses to the left of the goal.
47:02 Inswinging corner taken from the right by-line by Robin van Persie, James Tomkins manages to make a clearance.
46:44 Robin van Persie takes a shot. Save made by Robert Green.
45:59 Zavon Hines takes a shot. Save made by Wojciech Szczesny.
45:24 Francesc Fabregas has an effort from just inside the box that misses to the left of the target.
45:01 The match restarts for the second half.
Half Time
45:00+2:30 The referee blows for half time.
45:00+0:48 Inswinging corner taken right-footed by Samir Nasri from the left by-line, Robert Green makes a save.
45:00+0:27 Johan Djourou takes a shot. Save by Robert Green.
43:45 Foul by Carlton Cole on Theo Walcott, free kick awarded. Emmanuel Eboue takes the direct free kick.
42:59 Corner taken by Wayne Bridge, Francesc Fabregas makes a clearance.
42:44 Carlton Cole takes a shot. Johan Djourou gets a block in.
40:18 Assist by Robin van Persie.
40:18 GOAL - Theo Walcott:West Ham 0 - 2 Arsenal Theo Walcott gets on the score sheet with a goal from close range high into the middle of the goal. West Ham 0-2 Arsenal.
37:43 Corner taken right-footed by Samir Nasri from the left by-line, clearance by James Tomkins.
36:41 Carlton Cole concedes a free kick for a foul on Laurent Koscielny. Direct free kick taken by Gael Clichy.
31:48 Short corner worked by Robin van Persie.
31:27 Robin van Persie has an effort at goal from deep inside the box striking the post.
27:53 Alex Song takes a shot. Blocked by James Tomkins.
26:54 Jonathan Spector fouled by Johan Djourou, the ref awards a free kick. Direct free kick taken by Luis Boa Morte.
26:02 Foul by Robin van Persie on Luis Boa Morte, free kick awarded. Free kick taken by Matthew Upson.
23:09 Carlton Cole takes a shot. Save made by Wojciech Szczesny.
22:53 Samir Nasri takes a shot. Save by Robert Green.
22:21 Zavon Hines produces a left-footed shot from inside the six-yard box that clears the bar.
22:01 Carlton Cole takes a shot. Save made by Wojciech Szczesny.
19:17 Substitution Luis Boa Morte joins the action as a substitute, replacing Mark Noble.
18:18 Theo Walcott takes a shot. Comfortable save by Robert Green.
16:34 Francesc Fabregas produces a right-footed shot from outside the penalty box and misses wide left of the target.
14:57 Julien Faubert concedes a free kick for a foul on Francesc Fabregas. Free kick crossed right-footed by Samir Nasri from left
wing, Robert Green makes a save.
14:57 Booking The referee shows Julien Faubert a yellow card for unsporting behaviour.
12:55 Assist on the goal came from Theo Walcott.
12:55 GOAL - Robin van Persie:West Ham 0 - 1 Arsenal Goal scored by Robin van Persie from deep inside the penalty box to the bottom right corner of the goal. West Ham 0-1 Arsenal.
11:50 Mark Noble takes a inswinging corner from the left by-line played to the near post, clearance made by Robin van Persie.
7:54 Samir Nasri takes a shot. Save by Robert Green.
7:15 Francesc Fabregas fouled by Mark Noble, the ref awards a free kick. Direct free kick taken by Robin van Persie.
4:44 The referee blows for offside. Matthew Upson restarts play with the free kick.
2:04 Handball by Radoslav Kovac. Robin van Persie fires a strike on goal direct from the free kick.
1:30 Corner taken right-footed by Samir Nasri, Matthew Upson makes a clearance.
0:00 The game gets underway.
Live text and data provided by The Press Association.
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