The Germany striker netted once in each half after a fine opener from Aaron Ramsey as Arsene Wenger's men remained on course for Champions League qualification.
In a dress rehearsal for the FA Cup final between these teams in May, the Gunners were comfortable victors in a physical Premier League encounter, with Lukas Podolski scoring twice.
After Aaron Ramsey finished off a fine attacking move to sweep home half an hour into the game, the German netted once in each half to cap off a solid afternoon's work for Arsene Wenger's men.
Nikica Jelavic and Podolski went close after a quiet opening 15 minutes but both were denied by good saves.
At the other end, Shane Long was guilty of wasting an excellent chance, and the visitors made him pay six minutes later. A crisp passing move culminated in Mesut Ozil, back after a hamstring injury, combining with Santi Cazorla to find Ramsey and the Wales international hit the target with a low finish.
Hull went agonizingly close to levelling four minutes later as Jake Livermore picked up a loose ball and unleashed a long-range strike that beat Wojciech Szczesny, but struck the post before bouncing to safety.
Arsenal doubled its lead in first-half stoppage time through Podolski, although a cluster of Hull players felt that Jelavic had been fouled by Mikel Arteta in the build-up. The German timed his run into the penalty area perfectly to lash home after Ramsey had cushioned Giroud's cross on his chest.
Wenger's side made it 3-0 nine minutes after the break. Cazorla teed up Ramsey on the edge of the area and the midfielder's effort was saved by Harper with his feet but the ball fell to Podolski, and he calmly fired home from seven yards.
The visitors were very nearly gifted a fourth in the 64th minute as Harper misjudged a back pass from James Chester. Giroud blocked the goalkeeper's clearance and struck the crossbar from a tight angle.
Mertesacker was next to go close as he met a 75th-minute free kick from Cazorla but his looping header was just too high.
Ramsey missed a late chance to net his second but it didn't matter as Arsenal completed a comfortable win over its FA Cup final opponent, taking another step towards securing Champions League football for next season.