Matt Godden headed his fourth goal of the season as Coventry picked up three points on the road at struggling Hull.
The Sky Blues striker found the net from Ian Maatsen's ninth-minute cross in the first league meeting between the two sides since March 2012.
And although the Sky Blues failed to add to their lead, with Viktor Gyokeres having a curling effort saved by Matt Ingram and then firing just wide after the break, Hull's lack of potency in front of goal again cost them dear.
Coventry remain in fourth place, but their eighth win of the season moved them to within one point of West Brom, who lost to Fulham in Saturday's early kick-off.