The Gunners failed to take advantage of a side hit by suspension and injuries despite taking a first-half lead.
Boro manager Gareth Southgate would have derived more satisfaction from this game than his counterpart.
Southgate, in fact, has never lost to Arsenal since he took over as Middlesbrough's manager.
Arsenal were strong favourites to win the game against a side without the suspended David Wheater and several injured players.
Arsenal threatened when Adam Johnson gave the ball away and Abou Diaby shot wide with a horrible shot. A few minutes later Ross Turnbull saved with his legs from Diaby.
Arsenal went ahead after 17 minutes through Emmanuel Adebayor who rose in a crowd of players to head the ball past Turnbull. Southgate would not have been happy with the slack marking of his defence.
Boro drew level after 29 minutes with a brilliant header from Jeremie Aliadiere. When Tuncay crossed from the left the former Arsenal player connected with a flying header that left Manuel Almunia helpless.
The goal lifted Boro and there were strong appeals for a penalty when Gael Clichy brought down Johnson with a clumsy challenge just inside the box.
Television replays showed it was a penalty but the referee waved on play.
Middlesbrough were playing with tremendous spirit at this stage even though Robin van Persie missed a close-range chance to put Arsenal ahead with a quick counter-attack.
Arsenal manager Arsene Wenger could not have been happy with the first-half performance of his side.
Just after the break Diaby was booked for a foul - the only caution in the game.
Almunia made a brilliant save from a fierce Stewart Downing shot while at the other end van Persie shot across the face of the goal.
Boro, who had four products from their highly-rated academy in their side, were putting in a spirited performance.
But there was a lack of authority and flamboyance from the visitors and there were no big-name characters in their side to provide any inspiration.
Turnbull saved at the near post from substitute Nicklas Bendtner as Boro earned a point in their fight to keep away from the relegation zone.