Theo Walcott's excellent 94th-minute cross found the hard-working Emmanuel Adebayor who seemed certain to score from five yards out only to hit the crossbar with a close-range header.
It was tough on Arsene Wenger's side who had moved up the gears after the interval following a very tight and cagey first period.
But it was a typical display by the Rossoneri on their travels as they showed why they remain the team to beat in Europe.
Last season's success brought their record in the Champions League to five trophies in the last two decades and their seventh in European Cup history.
Arsenal started the match brightly but suffered an early blow when Kolo Toure picked up a calf injury after tangling with Alexandre Pato and had to be replaced by Philippe Senderos.
Jens Lehmann was forced to make a sharp save to keep out Paolo Maldini's header as Carlo Ancelotti's side made a rare early foray forward.
The Gunners fashioned a half-chance of their own in the tenth minute when Emmanuel Eboue's cross appeared to be perfect for Adebayor.
However, the ever-diligent Alessandro Nesta did just enough to put the Togo man off and the ball ran through to Zeljko Kalac in the Milan goal.
However, after Arsenal's early zest, the first half settled into a cautious encounter.
Mathieu Flamini fired in a rare shot on goal eight minutes before the interval after being found by Eboue but the shot was easily saved by the under-worked Kalac.
However, Arsenal started the second half extremely well and they almost broke the deadlock when Fabregas' corner caused chaos in the Milan defence with the ball eventually coming off Kaka's chest and whistling just past the post.
Alex Hleb then burst into the area and pulled the ball back for Eboue who dragged his shot wide before Adebayor had a goal disallowed for offside.
The Gunners continued to attack and the disappointing Eduardo fired over the bar after working a neat one-two with Fabregas.
Milan had chances of their own and Massimo Oddo was given acres of space only to then fire wide when he should have done much better.
Arsenal piled on the pressure in the closing stages but Milan refused to buckle and will be the happier side going into next month's second leg at the San Siro.