The Gunners created a host of chances in a one-sided clash but were unable to make the breakthrough, with Hull goalkeeper Eldin Jakupovic in outstanding form.
Jakupovic made a string of fine saves, including one fine fingertip on to the post from a Joel Campbell free-kick, while Arsenal also had two penalty appeals turned down.
Both sides made numerous changes - nine by Arsenal by 10 for Hull - indicating priorities lay elsewhere, but the teams were fully committed. In all Arsenal had 24 shots to their opponents' six as they continually pressed, but Hull's performance was one of great resilience.
Another Championship side, Reading, provided the upset of the day as they came from behind to beat Premier League West Brom 3-1.
After a goalless first half, Darren Fletcher looked to have put the Baggies on course for the quarter-finals when he broke the deadlock in the 53th minute.
But Paul McShane grabbed a quick reply as he headed home from an Oliver Norwood free-kick and Michael Hector repeated that feat to put the Royals ahead 18 minutes from time.
Saido Berahino and Fletcher had late chances as West Brom sought an equaliser but Chelsea loanee Lucas Piazon settled it in injury time.
Everton kept their season alive as goals from Ross Barkley and Romelu Lukaku fired them into the quarter-finals with a 2-0 win at Bournemouth.
Barkley struck early in the second half with a heavily-deflected strike and Lukaku wrapped up the victory with his 21st goal of the season.
They were also indebted to goalkeeper Joel Robles, who kept out a first-half penalty from Charlie Daniels to keep the sides level at the interval.
Watford saw off Championship Leeds courtesy of an own goal from Scott Wootton early in the second half.
Wootton miscued a clearance and turned into his own net from a Ben Watson cross after 53 minutes.
Leeds were unable to get back into the game and Etienne Capoue, who earlier had a goal disallowed, spurned a late chance to make Watford's victory more convincing.