A first-half header from Emmanuel Adebayor saw the visitors in front at half-time and despite a second-half equaliser from Daniel Cousin, Hull were condemned to their fifth straight league defeat as both Samir Nasri and substitute Nicklas Bendtner found the back of the net in the last ten minutes.
Arsenal nearly found themselves in front early on when a blistering Robin van Persie free-kick from just outside the box saw the ball deflect off Michael Turner's outstretched leg and brush just past keeper Boaz Myhill's right-hand post.
A foul by Ian Ashbee on Emmanuel Eboue then gave van Persie another chance to practice his close-range free-kicks.
This time the Dutchman's calculated left-footed strike saw Hull's Myhill produce a top-class save as he managed to tip the fizzing ball onto the crossbar.
Arsene Wenger's men then took the lead on the half-hour mark as a curling van Persie corner saw Adebayor leap above Turner to head the ball into the bottom corner of the net from eight yards.
Hull were back on level terms on 65 minutes as Bernard Mendy controlled at long ball down the right and sent in a curling cross onto the head of the unmarked Daniel Cousin, who buried the ball past the outstretched Manuel Almunia and into the top corner of the net.
However, the visitors were back in front with ten minutes left as slick passing from Bendtner and van Persie found Nasri in space on the left side of the box.
The France international had time to pick is spot as he sent the ball into the bottom corner of the net with a pinpoint strike.
Arsenal were then 3-1 in front on 86 minutes as calls of offside against van Persie were ignored allowing the dangerman to slip the ball across the box to substitute Bendtner, who calmly slotted his effort past the hapless Myhill from six yards.
It could have been worse for Hull as Bendtner was presented with another chance moments from the end, but the Danish frontman was denied a second by Myhill's right-hand post.