Michael Chopra netted the Black Cats' second goal in the derby
Sunderland substitute Daryl Murphy headed home a dramatic injury-time winner to sink Middlesbrough in an absorbing Wear-Tees derby.
Tuncay calmly drove Boro ahead inside the fourth minute before Danny Higginbotham headed Sunderland's equaliser just two minutes later.
A minute before half-time Michael Chopra fired home before Afonso Alves' low shot levelled again for Boro.
Murphy headed home at the death to ensure Sunderland's top-flight safety.
With the Black Cats slumping to defeat at Newcastle last week and Middlesbrough losing to Bolton, both sides knew the importance of victory.
And the game exploded into life within the first six minutes, with Boro taking the lead with their first real threat.
Roy Keane says his players and staff deserve all the credit
Alves picked out Tuncay with a precise pass over the static Sunderland defence, and the Turkish striker calmly chested the ball down before rifling past Craig Gordon.
The Black Cats hit back immediately, with a well-worked leveller, before Boro had any time to guard their lead.
Defender Higginbotham pushed forward, rising to meet Danny Collins' cross from the left, and his expertly-guided header looped over Brad Jones into the corner of the net.
Both sides were positive, and Chopra did well beat the Boro offside trap only to shoot across the face of goal from an acute angle.
The influential Tuncay almost headed a second in the 27th minute, but his effort was just inches wide after Stewart Downing supplied an inviting cross.
The pace of the game did not abate as both sides continued to attack, with the Black Cats enjoying the better of the possession.
Southgate admitted the players were 'hurt' by the defeat
Chopra and David Wheater were at the centre of a flare-up when the Sunderland forward made a late challenge, with both players earning cautions as a result.
But it was the busy Black Cats striker who got the better of his opponent with the break looming.
Liam Miller found Chopra with a long ball and, after evading Wheater's challenge in the danger area, the former Newcastle United man blasted a left-foot shot in off the woodwork to calm Sunderland's nerves.
Jones had to be alert for Boro just after the restart to scoop the ball away from the foraging Kenwyne Jones, as Sunderland looked to add a third.
With the hosts in the ascendancy, Chopra again got beyond the Boro defence but he lacked composure with his shot.
Sunderland striker Jones required several minutes of treatment after suffering a blow to his head in a clash with Emanuel Pogatetz.
Chopra was denied at close range by Jones as the second half proved to be equally absorbing.
Gordon made a smart double save from Downing as Middlesbrough pressed, only for Alves to equalise seconds later.
The Brazilian, lurking unmarked, slid the ball under Gordon from close range, with the home defence failing to pick him up.
But Murphy, who had been on the pitch for just seven minutes, rose above the Boro defence to glance home Grant Leadbitter's corner, grabbing one of the most dramatic winning goals in the Stadium of Light's relatively brief history.
• Sunderland manager Roy Keane:
"It was a cracking game, which summed up our season.
"We've scored great goals this season and with the players we have we'll always be likely to score late on.
"We've had many setbacks - we showed the desire needed here today and you always get your rewards in football."
• Middlesbrough manager Gareth Southgate:
"It was cruel to lose a late goal but I can't fault the effort of the players today.
"Mistakes have cost us and we're disappointed but we have two home games left so we'll lift ourselves again.
"It's hard to lose a local derby but I've got a great group of players - this setback will make us stronger."
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