They are now a point behind Manchester United while third-placed Chelsea are closing in too.
Having been the only team to take three points from the Gunners in the league this season, Gareth Southgate's side set themselves up for a famous double after 25 minutes, albeit in controversial fashion.
They scored against the run of play when a ball forward was met by Tuncay. Jeremie Aliadiere was alongside the Turkish star but was in an offside position.
The linesman's flag stayed down though and Tuncay accelerated into the box as the former Gunner peeled away to get into position to meet the resultant cross and redirect the ball into the net from five yards out.
All was going to plan as far as the visitors were concerned. Southgate had set his team up to defend in numbers and hit the Gunners on the break.
The resistance was determined and, with the pace of Aliadiere and the guile of Tuncay, the counter-attack threat was a worry.
Better officiating in the opening minutes too could also have put a completely different complexion on the match.
Emmanuel Adebayor showed a cool head to slot the ball past Mark Schwarzer after only five minutes, but his goal was chalked off for offside.
True, the Togo striker was in an offside position when he received the ball, but he was put in possession by Boro's George Boateng.
Adebayor's protestations fell on deaf ears and all the early signs pointed to it not being Arsenal's day, particularly as they needed a win to climb back above Manchester United in the table.
The Gunners had their chances. Emmanuel Eboue hit the bar, while Adebayor and Cesc Fabregas had efforts that were too tamely struck to worry Schwarzer.
The Australian keeper had more of a challenge with an Eboue shot that he could only half-clear after 15 minutes and, seconds earlier, Robin van Persie should have converted a volley from just six yards out, but instead completely mis-kicked his effort.
Middlesbrough stuck to their game plan in the second half and stood firm under increasing pressure from the Gunners.
Arsene Wenger made a double substitution on the hour by bringing on Theo Walcott and Nicklas Bendtner for van Persie and Bacary Sagna.
Crosses began to immediately rain in on the Boro goal and Bendtner headed high and wide from one such delivery when he really should have hit the target.
Schwarzer kept his team ahead on 67 minutes when Fabregas was through on goal.
However, the Boro keeper was quick to narrow the angle and spread himself well to save with his legs.
Fabregas went close again seven minutes later when his header from Adebayor's cross bounced off the right upright with the visitors keeper beaten.
Wenger's team were camped in the Boro half for most of the remainder of the game, but they could not find a way through.
The visitors were resolute in defence and the Gunners seemed to want to walk the ball into the net.
However, the breakthrough finally came on 86 minutes when Kolo Toure rose highest to meet a Fabregas corner. He powered his header towards goal but the ball took a deflection off Andrew Taylor before going in off Schwarzer.
The temperature in the ground rose even higher just seconds later when Mido kicked Gael Clichy in the head and was shown a red card after only being on the pitch for nine minutes.
Arsenal lay siege on the visitors goal but, despite going close, could not find a dramatic winner.