Tuncay was handed two goals on a plate as Villa fell apart at the back
Tuncay profited from two shocking defensive errors to give Middlesbrough victory at Aston Villa and send them up to eighth in the Premier League.
He struck first after 34 minutes, lashing home from six yards after Nicky Shorey failed to clear a cross.
The hosts hit back within three minutes through a Steve Sidwell header.
But, after Afonso Alves had somehow missed for Boro from three yards, Sidwell's dreadful back pass set up Tuncay to score an 88th-minute winner.
Villa went into the game with their eyes on moving into the Champions League places at the expense of Manchester United but ended with nothing after a game dominated by expensive mistakes.
The hosts were the first to show, with Ashley Young robbed as he was about to pull the trigger and Gabriel Agbonlahor having his follow-up shot blocked.
We passed 'huge test' - Southgate
It took a loose pass, intercepted by Justin Hoyte, to get Boro on the front foot but when he was tackled and the ball fell to Stewart Downing, the England man shot wide.
Villa nearly broke the deadlock just before the half-hour mark when Young's free-kick took a wicked deflection off the wall but Ross Turnbull did well to adjust his feet before tipping the ball over the bar.
And it was the visitors who went in front five minutes later after a moment to forget for Shorey.
The defender made a terrible mess of trying to chest away Downing's diagonal cross into the area and Tuncay was on hand to belt the ball past the helpless Brad Friedel from six yards out.
O'Neill angered by 'two poor goals'
But Boro were unable to protect their lead for long and after Young and Agbonlahor had shots blocked the ball fell to James Milner and his chipped cross was nodded in by Sidwell.
The visitors ended the half on top with Downing twice drawing saves from Friedel with long-range efforts, while Alves was narrowly wide from eight yards after some slick passing in the area initiated by a cute reverse ball from Boro's England winger.
Presumably Villa boss Martin O'Neill was at his spiky best during the break because his side lifted the tempo straight from the restart.
Agbonlahor immediately burned Chris Riggott for pace on the outside but Turnbull stood up well to deny the flying Villa striker at the near post.
Soon after Sidwell headed over, while Milner was then denied by Turnbull's legs from Barry's cut back after Shorey's precise pass had carved Boro open down the left.
With just under half an hour remaining O'Neill withdrew defender Shorey and brought on striker Marlon Harewood as he went in search of all three points.
But it was Boro who created the better chances with Young heading Riggott's header off the line before Alves somehow missed from three yards after Friedel had palmed out Didier Digard's skidding 25-yard drive.
It was a dreadful miss and the Brazilian - Boro's record signing - was immediately hauled off to sit, head buried in hands, on the bench.
It looked as though the match was headed for a draw but with the final whistle looming Sidwell produced the last of the hat-trick of howlers and Tuncay was on hand to joyously rifle the ball past a stunned Friedel.
Aston Villa manager Martin O'Neil: "The one towards the end of the game obviously gives us little time to try and fight back but we should never have been in that position.
"We didn't play well today, we should have done better and we shouldn't have lost the game.
"We had a number of chances in the second half and had we taken one of those it would have worked in our favour."
Boro boss Gareth Southgate: "It was a good game of football. I'm really pleased with the way we passed the ball today and we created lots of chances for an away side.
"It was a huge test but we wanted to challenge ourselves. We've had a couple of good results - could we build on that or were going to be prepared to just settle for that and keep pulling results out when we were in trouble?
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