Alexis Sanchez gave the Gunners an early lead at the KCOM Stadium and although he missed a penalty after the dismissal of Jake Livermore, he netted one of three second-half goals as Theo Walcott and Granit Xhaka also got on the scoresheet.
Both teams started brightly but the first chance of the game did not arrive until the 13th minute when Sanchez blazed a shot over the bar for Arsenal after being found by Walcott.
However, they did not have to wait long before taking the lead as Sanchez got the final touch to an Alex Iwobi shot, with the deflection proving decisive in taking the ball over goalkeeper Eldin Jakupovic.
Just before the half-hour mark, the Tigers stopper kept his side in the game with an instinctive block to deny Iwobi, before Mesut Ozil sent the ball over the crossbar from close range.
Hull finally registered their first shot on target when Robert Snodgrass curled the ball too close to Petr Cech from inside the penalty area, before his team were reduced to 10 men during a dramatic end to the first half.
Livermore prevented Francois Coquelin's goalbound effort from finding the bottom corner but from the resulting spot kick, Jakupovic dived to his right to save from Sanchez.
Early in the second half, Santi Cazorla was perhaps fortunate to avoid a second yellow card for an infringement on Snodgrass, and Arsenal capitalised soon afterwards with a second goal.
After picking up the ball around 30 yards from goal, Walcott played a neat one-two with Iwobi before clipping his shot over Jakupovic and into the net, despite the best efforts of Harry Maguire.
Arsenal continued to dominate the game without creating any opportunities of note, but with 11 minutes left they were made to pay for resting on their 2-0 lead.
Substitute Dieumerci Mbokani got on the end of a through-ball before being taken out by Cech inside the penalty area, and after initially not giving the decision, the referee eventually pointed to the spot after speaking with his assistant.
Snodgrass stepped up to send Cech the wrong way from 12 yards, but within four minutes Arsenal re-opened their two-goal lead as Sanchez found the top corner after Walcott had seen an effort saved by Jakupovic.
It appeared that the scoring was complete but deep into added-on time, Xhaka netted his first goal in an Arsenal shirt with an unstoppable strike from 30 yards that found the roof of the net.body check tags ::