Ajax's injury-hit young side pulled back an early deficit to cast doubt on Arsenal's hopes of reaching the Champions League quarter-finals.
Arsenal, Ajax and Valencia all have five points and Arsenal must travel to Ajax and Valencia in their last three games.
The Premiership champions had only themselves to blame, as they finished their fourth successive Champions League home game without a victory.
Centre-back Sol Campbell summed up their feelings. He said: "It's very frustrating to keep dropping points at home after picking them up away.
"Things just didn't fall for us in the box. Tonight's results have made the group very tight, but Ajax have to come out and try to win in Amsterdam and that might help us." Arsenal's elaborate build-up was in sharp contrast to Ajax's simple pass and move football. Ajax blocked off space for Thierry Henry and closed down Arsenal in midfield. Ex-Ajax hero Dennis Bergkamp made a bright start, then faded against his old club.
Arsenal wasted a stream of free-kicks and corners, especially in the second half. Their strikers preferred to play outside the penalty area rather than make runs into the Ajax box and compete with defenders.
The Dutch side might even have won when substitute Nourdin Boukhari reached a deflected late cross ahead of substitute goalkeeper Stuart Taylor, only to bundle the ball wide.
Yet the game started so well for the Gunners. After only five minutes, Bergkamp sent Sylvain Wiltord clear on the right to drive a low shot past keeper Bogdan Lobont for the opener.
Ajax refused to be phased. Twelve minutes later, Tomas Galasek's diagonal pass split the Arsenal defence for Nigel De Jong to control and beat David Seaman with a crisp left-foot finish.
Arsenal's remaining chances were few. Gilberto Silva snatched at a near-post effort after a mistake by Lobont.
Bergkamp fired against the outside of a post and substitute Kanu shot over in a late raid, but Ajax coach Ronald Koeman will surely be more pleased with the result than Arsene Wenger.