Arsenal lie second in the league table with 70 points, three adrift of leaders Manchester United, who face Aston Villa later in the day,
At the Reebok stadium, Matthew Taylor put the hosts in front after 14 minutes when he rose unchallenged to head home Gretar Steinsson's cross.
Matters went from bad to worse for Arsenal when Abou Diaby was sent off in the 31st minute for planting his studs on Steinsson leg.
Taylor heaped more misery on the Gunners when he doubled Bolton's lead two minutes before the break, side-footing a shot into the corner of the net.
Arsenal did not give up and managed to produce a remarkable comeback.
French defender William Gallas narrowed the gap in the 63rd minute with a close-range finish.
Dutch striker Robin van Persie claimed the equalizer five minutes later after converting a penalty.
Few minutes before the final whistle, Jlloyd Samuel deflected Cesc Fabregas shot into his own net to give Arsenal a valuable win.