Paul Clement believes Swansea have rediscovered the momentum to win their Premier League survival battle.
Swansea ended a desperate run of one point from six games by beating Stoke 2-0 at the Liberty Stadium, Fernando Llorente and Tom Carroll the men on target either side of half-time.
Hull remain two points above Swansea in 17th place after beating Watford 2-0, but Clement feels the momentum has shifted back towards his side.
"I felt a more positive, vibrant dressing room," Swansea head coach Clement said.
"Everyone knows that they put in a good shift physically, and played well tactically and technically.
"Hopefully it give us that impetus to go on and finish really strongly.
"Yes, we are two points behind Hull and they are in the driving seat.
"But we're right behind them, breathing down their necks, and we'll do that to the very last game."
Clement had called the contest a "must-win game" before kick-off as he predicted that Hull would beat Watford at home.
The Tigers did that, despite having striker Oumar Niasse red carded after 25 minutes with the game goalless.
"It's the first time I've called it as a must-win game and I was right," Clement said.
"If the gap had gone to five points with four games left I think it would have been very difficult for us.
"Although the points difference hasn't changed between us, what has changed is that we've put that poor run of form behind us.
"We've picked up very few points in the last six games and hadn't been performing that well either.
"Today's changed it. That's important psychologically going into the next four games, and the next one is a big test at Man United.
"We've got our confidence back, not just that we've won this game, but the nature of how we won the game."
Stoke manager Mark Hughes bemoaned Marko Arnautovic's missed second-half penalty as the turning point.
Arnautovic sent his 69th-minute spot-kick, awarded for Federico Fernandez shoving over Xherdan Shaqiri, high over the crossbar moments before Carroll's deflected drive.
"The second half we were the more dominant side, but obviously the match-defining moment was the penalty," Hughes said.
"It needs to go in from our point of view because the apprehension in the stadium would have risen and we would have benefited from that.
"But we missed, and they go down the other end and score from a deflected shot.
"At 2-0 it's obviously very difficult for us, but I was disappointed with how we started the game.
"We talked about that beforehand because we wanted to affect Swansea's confidence level, which was low given their recent run, by starting brightly.
"But they scored from their first corner. We were in the right position, but we didn't challenge for the ball, and in that area you need to get your head on it."