Keane produced two fine finishes in the first half
Robbie Keane scored his first Premier League goals for Liverpool as they beat West Brom to go three points clear of Chelsea at the top of the table.
A combination of Scott Carson's body and Jonas Olsson's arm prevented Yossi Benayoun's shot opening the scoring.
But there was no stopping Keane when he latched on to Steven Gerrard's pass before clipping the ball over Carson.
Keane scored his second goal when he rounded Carson and slotted home before Alvaro Arbeloa curled in a late third.
Keane will be delighted to get off the mark in the league, following his £20m summer move from Tottenham.
And the Republic of Ireland international took his goals well as Liverpool made sure there would be no repeat of the collapse that saw them lose a lead and fall to defeat at Spurs a week ago.
It helped that this time they were up against a team in West Brom who have not won at Anfield for 41 years.
Once Liverpool went ahead, it never looked as though the visitors would bring an end to that poor run.
The Baggies did make a decent start to the match, enjoying more of the possession, but as soon as Liverpool kicked into gear, they took control of the match.
Keane had the first opening, but shot tamely after Javier Mascherano had prodded the ball through to him.
As Liverpool pressed, the lively Benayoun, starting in place of Xabi Alonso, went close to a goal when he saw his shot hit Carson and then Olsson's arm.
A goal for Liverpool looked inevitable and when Gerrard rolled the ball into the path of Keane, he finished off the move with a deft strike.
Mowbray takes positives for Baggies
Nine minutes later, Keane latched on to Fabio Aurelio's pass, took one touch to go past the onrushing Carson and passed the ball into an empty net with his second touch.
From the sidelines, Fernando Torres - back on the bench after a six-game absence because of injury - would have been impressed with his strike partner's clinical finishing.
There was a sense that Liverpool took their foot off the gas after the interval, while West Brom toiled as they attempted to get themselves back in the game.
Had Ishmael Miller shown a better touch, he might have given the Baggies a lifeline but his poor control when clean through meant a rare chance went begging.
Benitez delighted for 'brilliant' Keane
On 72 minutes, Liverpool replaced goalscorer Keane with Torres, with both players receiving rapturous applause from the home fans.
Torres had little chance to make an impact, as Liverpool coasted, but the Spaniard will be relieved to have made his comeback.
In the final seconds, Arbeloa scored with a curling left-foot shot to seal the win, which sees Liverpool leapfrog Chelsea at the top of the table, with the Blues playing at Blackburn on Sunday.
Liverpool boss Rafael Benitez:
"I have had no doubts that he would start to score regularly for us.
"Robbie has told me he has got a monkey off his back, not an expression I had heard before but I understand it.
"It was only a matter of time before he scored in the league. He is quick and can punish any mistakes that defenders make, and that is what he did."
West Brom manager Tony Mowbray:
"We intended to be positive, to ask Liverpool some questions and go for it."We intended to be attack-minded and for long spells we held our own.
"We had a sloppy 10 minutes and we were punished for that.
"But we had some young strikers out there against top-class defenders. They were a little naive at times."
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