A fine solo goal from Peter Odemwingie guided Stoke City to a third straight Barclays Premier League victory.
The 32-year-old capitalised on an error by Ahmed Elmohamady and drove home a low shot in the 62nd minute for his fourth goal for the Potters.
The win, following previous successes against West Ham United and Aston Villa, moved Stoke to within six points of ninth-placed Newcastle United, while Hull are still looking over their shoulder in 14th, seven points above the relegation zone.
There were few clear-cut chances in the first half with the best opportunity falling to Hull's Liam Rosenior, who headed wide when unmarked inside the penalty area.
The hosts improved after the break, however, and Odemwingie's individual brilliance ensured a fourth win in five league matches for Stoke, while inflicting a second straight loss on Steve Bruce's men who were beaten 2-1 at West Ham on Wednesday.
The sides proved evenly matched in the opening exchanges, but it was the visitors who fashioned the first chance on goal in the 10th minute as Tom Huddlestone's low 20-yard drive forced Asmir Begovic into a smart stop.
Stoke were then handed a huge reprieve four minutes later when Shane Long's superb cross reached Rosenior, who headed over the bar.
At the other end, Odemwingie's shot from the edge of the area was the hosts' best effort before the break.
Stoke showed more urgency in the early stages of the second half with Odemwingie testing Hull's stand-in goalkeeper Steve Harper for the first time before Peter Crouch's half-volley flew wide.
Despite the second-half improvement, Stoke were thankful to Begovic shortly before the hour mark as he tipped away David Meyler's deflected shot with Nikica Jelavic unable to make the most of the follow-up opportunity.
That save proved crucial as Stoke moved ahead shortly afterwards. A poor pass from Elmohamady was collected by Odemwingie who charged through the Hull defence and drove past Harper for his third goal in as many Premier League matches.
Stephen Ireland went close to a second in the 75th minute with a stinging drive but one goal proved enough to settle the encounter.
Stoke City manager Mark Hughes: “It was an important win for us, despite not being able to hit the heights of our performances against West Ham and Aston Villa.
“You have to give the opposition some credit because they came here and made it very difficult for us by putting players behind the ball and made it hard for us to penetrate them in-behind.
“We found it really difficult to unlock them during the first 45 minutes, but I thought we were much better in the second half, particularly once we had made the initial breakthrough.
"All in all it is very satisfying because we didn’t play as well as we have done in recent weeks, but we were able to get the job done and reach the 40-point mark.”
Hull City manager Steve Bruce: "The one thing a manager or coach can't eradicate is a mistake. Unfortunately Elmo's (Elmohamady) made a horrible one today which he regrets and it's cost us the game.
"We've prided ourselves on being difficult to play against and difficult to beat and that's got us to the situation we're in at the moment. But unfortunately (if) you make mistakes at this level (you get punished). You might get away with it in the Championship, where we were last year.
"Odemwingie's still got a bit to do it's a great finish, but we've gifted them something when they never looked like breaking us down and causing us a problem.
"Until you're mathematically safe, everybody is still edgy. We've got ourselves into a wonderful position and I still think a couple of wins and a draw will be enough. But we've seen some crazy results today, you never quite know."
|05 Apr 2014||v Chelsea (A)|
|12 Apr 2014||v Newcastle (H)|
|19 Apr 2014||v Cardiff (A)|
|26 Apr 2014||v Spurs (H)|
|03 May 2014||v Fulham (H)|
|11 May 2014||v West Brom (A)|