Joao Pedro's goal helped Hull secure just a second home win of the season
Hull City ended a 13-game winless streak as substitute Mason Burstow's late goal saw off Swansea City and lifted the Tigers out of the Championship relegation zone.
Ruben Selles looked like being denied a first Hull victory in his third game in charge after Harry Darling's fine header cancelled out Joao Pedro's deflected opener.
But Hull were the better side throughout and Swansea, who produced arguably their poorest performance of the season, were deservedly beaten when Burstow picked off Lawrence Vigouroux's loose pass before beating the goalkeeper from 20 yards.
That meant a much-needed maximum for Selles' new team, who had not tasted victory since 1 October.
They climb from the bottom of the table to 21st, albeit with some of their relegation rivals in action later in the day.
But there was more disappointment for Swansea head coach Luke Williams, whose side drop to 11th having failed to muster any sort of response to last weekend's dispiriting defeat to Sunderland.
The MKM Stadium has been an unhappy hunting ground for Hull this season, yet they seized the initiative from the outset against sloppy Swansea to claim just a second home success this season.
Hull should have led earlier than they did, Regan Slater shooting wide when unmarked eight yards from goal.
They came even closer when Gustavo Puerta's fierce drive crashed off the post before rebounding off Swansea goalkeeper Vigouroux and looping just over the bar.
There was an element of luck about the opening goal when it came, as Pedro latched on to Steven Alzate's pass and saw his shot bounce inside the near post off Ben Cabango, yet there was nothing fortunate about Hull's lead.
Swansea had been dreadful, but hauled themselves back into the contest thanks to Darling's excellent header, the centre-back rising to power Josh Tymon's whipped cross into the bottom corner after a set-piece was only half-cleared.
Harry Darling's effort was Swansea's first headed goal this season
The equaliser failed to revitalise Swansea, who were lethargic throughout and were fortunate again when Matt Grimes' poor pass presented a chance to Pedro.
This time Vigouroux saved his team, getting a vital touch on the ball as he dived at Joao Pedro's feet before the striker's shot was blocked by Josh Key.
Swansea might then have gone in front from another set-piece, with Darling guiding Grimes' corner back across goal and Cabango heading against the post.
But Hull deservedly reclaimed the lead when Burstow capitalised on Vigouroux's error with a measured finish.
Selles' side might have put another layer of gloss on the win had Ryan Longman's late drive not come back off the post, but by then their job was done.
Hull head coach Ruben Selles:
"It was a powerful feeling [at the end]. The club, the fans, the players, the staff have been looking for that feeling long enough and we finally break [the run], so it was a really good feeling.
"I think we played a really good game. We were clear in what we wanted, we minimised our opponent which is really difficult. We were aggressive.
"The only time in the game we were not is when we conceded the goal. It was clear why we concede the goal – we lost control of the game because we started to kick long balls.
"But when we got to 2-1, we never gave the feeling of 'now we need to protect'. We did not retreat."
Swansea head coach Luke Williams:
"It was a really poor performance. The opposition were better than us. That's a big problem.
"But I don't quite know why we were miles off it - but we were.
"I can't say I jumped for joy when the ball hit the back of the net [for the equaliser] because from what I'd seen for the 40 minutes before that, we were well off the pace of the game.
"I think if we had got out of here with a point we'd have been very fortunate."
