Oumar Niasse boosted Hull's chances of avoiding relegation from the Premier League as the Senegal forward inspired a crucial 2-1 victory over Swansea, while Bournemouth won for the first time in 2017 thanks to Josh King's treble in a 3-2 success against West Ham.
Niasse, on loan from Everton, came off the bench to score twice in the second half at the KCOM Stadium on Saturday and Marco Silva's side are now just one point from safety.
After a tense first half, Niasse broke the deadlock in the 69th minute when he played a one-two with Abel Hernandez and drilled past Swansea goalkeeper Lukasz Fabianski.
Niasse sealed Hull's third win over Swansea in all competitions this season with a blistering strike from inside the penalty area in the 78th minute.
Alfie Mawson's 90th minute goal was no consolation for Swansea, who have lost their last three away games and are only three points above third bottom Hull.
"We got three important points, so of course I'm happy," Silva said.
"It was a tough game. We improved in the second half and after that we controlled the game."
At Dean Court, Bournemouth overcame two missed penalties and a late equaliser to end their nine-match winless run in all competitions.
King had netted with a penalty in last weekend's draw at Manchester United, but the Bournemouth striker fired wide with another spot-kick in the early stages against the Hammers following Sofiane Feghouli's foul on Charlie Daniels.
Just 48 seconds later, West Ham winger Michail Antonio marked his return from suspension with a cool finish after taking Feghouli's pass and spinning away from his marker in the 10th minute.
King made amends for his penalty howler in the 31st minute when the striker flicked the ball up in the penalty area before firing home.
Remarkably, Bournemouth missed another penalty, this one awarded for Jose Fonte's foul on March Pugh late in the first half, as Benik Afobe's effort was saved by Darren Randolph.
- Perfectly placed -
King struck again in the 48th minute when his close-range effort from Afobe's flick-on was allowed to stand despite West Ham's appeals for handball.
West Ham's Andre Ayew tapped into an empty net from Sam Byram's 83rd minute cross, but King bagged the winner from close-range in stoppage-time to lift Bournemouth six points clear of the relegation zone.
"Relief is the overwhelming feeling," Bournemouth manager Eddie Howe said.
"Josh King has had an outstanding season and is beginning to show true potential."
Everton improved their prospects of a Europa League berth with a 3-0 win over West Bromwich Albion at Goodison Park.
Ronald Koeman's seventh placed team are just two points behind sixth placed Manchester United after recording their fifth successive home victory.
With British boxer and Everton fan Tony Bellew watching from the stands after his recent heavyweight success against David Haye, Kevin Mirallas landed the first blow for the hosts in the 39th minute.
Ross Barkley's shot was parried by Albion goalkeeper Ben Foster and Mirallas was perfectly placed to slot home.
Morgan Schneiderlin doubled Everton's lead on the stroke of half-time, the midfielder unleashing a ferocious strike for his first goal since a January move from Manchester United.
Romelu Lukaku sealed the rout with a header in the 82nd minute for his 19th league goal of the season.
Liverpool host Burnley on Sunday in the weekend's only other league action due to FA Cup quarter-final fixtures.