The Gunners had made it 1-0 early on through Andrey Arshavin but the home side were level on the half-hour mark thanks to a Jimmy Bullard penalty.
Hull were then down to ten men just before the break as George Boateng received his second yellow card of the game.
The match was then seemingly heading for a draw but a late mistake from Hull keeper Boaz Myhill allowed Nicklas Bendtner to claim all three points for the visitors with an injury-time strike.
Arsenal broke the deadlock on 14 minutes as Arshavin orced his way through the lacklustre Hull defence to bury the ball into the bottom right corner of the net from close range and register his ninth league goal of the season.
Hull were level on 28 minutes as referee Andre Marriner awarded the home side a penalty after Sol Campbell was adjudged to of brought down Jan Vennegoor of Hesselink inside the box.
Bullard took the resulting spot-kick and sent the ball into the top right corner of the net to grab his fourth goal of the campaign.
Phil Brown's side were then down ten men in first-half injury-time as Boateng picked up a second yellow card following a late challenge on Bacary Sagna.
Tigers youngster Liam Cooper had to come on to replace the injured Kamil Zayatte early in the second half after a strong challenge from Campbell left Guinea international unable to continue.
Bullard came close to scoring a spectacular goal midway through the second half but his run and shot from 30 yards saw the ball fly just over the Arsenal crossbar.
Arshavin should have had the Gunners back in the lead moments later as a run and cross from substitute Theo Walcott left the Hull defence stretched, but the Russia international failed to capitalise at the back post and sent the ball high and wide with a wild first-time effort.
Another cross from Walcott presented Bendtner with a chance late on for Arsenal but a last-ditch lunge from Cooper deflected the Danish forward's shot up and over the bar.
The visitors then did steal all three points in injury time as a long-range effort from Denilson was poorly parried by Myhill into the path of Bendtner, who made no mistake from close range to send Arsene Wenger's men up to second in the table.