Hull City moved level on points with Cardiff City, and three clear of the relegation zone, thanks to Keane Lewis-Potter's 14th-minute header.
After plenty of early possession, the visitors took the lead from a set piece when Lewis-Potter stooped down to add the final touch to a well-worked corner routine.
Despite having the vast majority of the ball for the rest of the contest, the Bluebirds failed to test Nathan Baxter in the Hull goal.
The hosts almost snatched a lead equaliser but substitute James Collins, who scored Cardiff's winner against Preston on Saturday, saw his injury-time header rebound off the post.