Emmanuel Adebayor headed the visitors in front after 17 minutes from Cesc Fabregas’s corner.
But Boro hit back and former Gunners striker Jeremie Aliadiere headed a fine equaliser from Tuncay Sanli’s fierce cross 12 minutes later.
Robin van Persie wasted a good chance after the break, while keeper Manuel Almunia parried Stewart Downing’s shot.
Arsenal boss Arsene Wenger will view this as two points wasted as they try to keep in touch with the title pace-setters – seeing his side dominate possession but fail to take advantage.
Boro boss Gareth Southgate saw his revamped defence hold firm in the closing stages to earn a valuable point.
Wenger’s side opened with real intent, with Van Persie shooting just wide after a glorious passing move and Abou Diaby forcing Boro keeper Ross Turnbull into a block at his near post.
And the Gunners took a deserved lead after 17 minutes, although Southgate will be furious at his defence for allowing Adebayor so much time and space to head home Fabregas’s corner.
Diaby then tested Turnbull again after another corner caused more problems, before Middlesbrough hit back with a surprise equaliser after 29 minutes.
Tuncay was the creator with an instant driven cross, with Aliadiere reacting first to get in ahead of William Gallas and flash a fine header beyond Almunia.
The visitors were given a reprieve by referee Peter Walton five minutes later when he waved away justified penalty appeals as Adam Johnson tumbled under a challenge from Gael Clichy.
The visitors re-asserted their supremacy after the interval, but Middlesbrough were always a threat on the break.
And it took a fine save from Almunia to turn Downing’s shot to safety after Arsenal had been caught out by a raking pass from Julio Arca.
But most of the action was at the opposite end, with Van Persie shooting across the face of the goal from Diaby’s pass and then blasting over.
Diaby shot straight at Turnbull as Arsenal enjoyed plenty of possession without creating many clear-cut opportunities.
The Gunners introduced Nicklas Bendtner in the closing stages, and he almost made an impact as he forced Turnbull into another block at his near post, then headed off target when well placed.
They were Arsenal’s final chances of a frustrating afternoon as Boro held out for a draw.