Jordan Rhodes scored his first goal since Boxing Day as Sheffield Wednesday beat Hull 1-0 at the KCOM Stadium.
After Allan McGregor had produced a good save to deny him in the opening stages, striker Rhodes headed Wednesday in front after 18 minutes on his return to the starting line-up.
Hull, who had scored nine goals in their last two matches before this clash, thought they had levelled things up in stoppage time when Abel Hernandez put the ball in the net, only for the linesman to raise his flag for offside after speaking to the referee.
After a couple of early City attacks had come to nothing, the Owls had the game's first clear-cut chance in the fifth minute when Adam Reach's searching left-wing cross was met by Rhodes at the back post, but home goalkeeper McGregor was on hand to beat his header away.
The Tigers went straight down the other end but were twice denied as Harry Wilson's effort was blocked before Owls keeper Joe Wildsmith came out quickly to clear the danger as Hernandez looked to get on the end of Jon Toral's dangerous through-ball.
Fernando Forestieri then sent a low drive towards goal after 10 minutes but it did not trouble McGregor.
Hull came close to opening the scoring against the run of play three minutes later when Max Clark let fly from 30 yards but Wildsmith got down well to turn the ball behind for a corner.
Wednesday broke the deadlock in the 18th minute when Jack Hunt picked out an unmarked Rhodes in the box and he headed the ball past McGregor from close range to score his first goal of the calendar year.
Reach had an opportunity to double the visitors' lead in the 26th minute after a defensive error saw the ball land to him but he sent his half-volley just wide.
Hull almost levelled things up on the stroke of half-time when Wilson's ball in from the left found the on-rushing Hernandez in the middle but Wednesday were able to scoop the ball behind for a corner.
The hosts began the second half brightly, with Toral firing a half-volley towards goal just a minute after the break but Wildsmith was equal to it.
Hernandez was thwarted just as he was about to pull the trigger after 73 minutes as Frederico Venancio put in a well-timed challenge in the box.
And Hernandez came close again two minutes later when his shot from around 20 yards went just over the bar.
Wednesday squandered a chance to double their advantage late on when a mix-up at the back allowed substitutes Marco Matias and Frederik Nielsen the opportunity to shoot but the ball was cleared off the line.
Hull continued to push forward in the closing stages and were denied an equaliser in injury time when an Hernandez goal was ruled out for offside before Angus MacDonald headed wide in the last of eight added minutes.
The managers
Nigel Adkins: "I've just watched it back on the replay now. We score a goal, the referee indicates a goal and points to the centre circle.
"The linesman runs towards the halfway line as they normally do when indicating a goal and obviously we're celebrating then.
"And one of the players has asked the referee to go and speak to the linesman. They've had a conversation and disallowed the goal for offside.
"They both actually gave a goal then they've come up with the decision that it's not a goal.It's very, very close. It doesn't matter whether I agree or disagree - it's given as offside and we lose the game. For me there was an opportunity today."
Jos Luhukay: "When we saw the last games from Hull, four and five goals scored while we lost the last two games, (we knew it would be) a very difficult game for us.
"The mentality and the character in my team is fantastic. Last Tuesday we lost three players for today - Atdhe Nuhiu, Lucas Joao and Daniel Pudil - but the players who came in did a very good job.
"As a team we are strong and we stay together. On Tuesday we lost as a team and today we won as a team and that makes me very happy.
"I think it was a good game. Of course for us, the first half was better than the second."