The Gunners dominated proceedings at the Reebok Stadium with Robin van Persie twice being denied by the woodwork but they failed to take a number of other chances.
With Newcastle beating Blackburn it meant Arsene Wenger's side dropped to seventh in the table, while Wanderers, still just above the drop zone, edged two points ahead of Rovers.
Arsenal have now taken just one point from their last three away matches, although they marginally improved on their defeat at the Reebok last season.
After earning six points from a possible nine in January Owen Coyle's side are playing with confidence and recorded their first clean sheet in 12 league matches dating back to November.
That was partly down to Arsenal's failure to take advantage of their dominance, particularly early on, and partly to the frame of the goal in front of the travelling support.
The Reebok Stadium witnessed virtually one-way traffic in the first 20 minutes.
Arsenal's best chance was their first when Van Persie had his header cleared off the line by David Wheater in only the ninth minute.
The home side, so organised and determined in their last league outing on this ground when they deservedly beat Liverpool 3-1, struggled to get a foothold as their opponents made all the running.
Wheater again denied Van Persie, this time by blocking his shot, after Theo Walcott had shrugged off Sam Ricketts to cross before the Holland international turned provider for Alex Oxlade-Chamberlain only for the youngster to blaze over from a good position.
Unusually Van Persie was wasteful after making some space on the edge of the penalty area and Adam Bogdan was relieved to see the ball sail over his crossbar.
From that point the Gunners' influence on the game began to wane and David Ngog should have made them pay by converting either of two good chances.
Having held off Laurent Koscielny his narrow-angle shot was parried away by Wojciech Szczesny but an even better chance went begging just after the mid-point of the half.
Wheater's knock-on left the Frenchman with only the goalkeeper to beat but although he achieved that his shot rolled past the far post.
Walcott had even more time with his chance after racing on to Oxlade-Chamberlain's through-ball but Bogdan did just enough to deflect the ball for a corner.
The second half began at a much more lively pace but again Arsenal gained the early upper hand with Mark Davies blocking Walcott's shot inside his own area.
Van Persie almost opened the scoring when his touch from Bacary Sagna's right-wing cross rebounded back off the near post while Koscielny headed wide the Dutchman's corner.
Aaron Ramsey was next to stab wide as Bolton continued to ride their luck inside their own penalty area.
Ngog almost got on the end of a Martin Petrov cross but was crowded out and it proved to be his last involvement as he was replaced by Kevin Davies.
With 10 minutes remaining Van Persie, for the second time in the half, was denied by the frame of the goal as his delicately-weighted chip had the beating of Bogdan but not the crossbar.
Szczesny's challenge on Mark Davies had the home crowd appealing for a penalty with a couple of minutes remaining but referee Chris Foy saw nothing wrong.
The midfielder also fired wide before the end as the hosts launched a last-gasp bid to snatch victory and it was they who left the field the happier after securing another point towards survival.