Jordan Ayew rescued a point for Swansea as their dominant display could only muster a 1-1 draw at home to a lacklustre Everton side.
For all of Swansea's early endeavour, Everton took the lead in fortuitous circumstances just before half-time when Kyle Naughton inadvertently headed the ball into his own goal (43).
The hosts levelled after the break through Ayew (71), who marked his return from a three-match suspension with a fine half-volley into the far corner.
Seamus Coleman and Tammy Abraham spurned opportunities for both sides late on as the match ended all square, leaving Swansea five points above the relegation zone with five games remaining.
Swansea started brightly, but were denied twice in quick succession as Jordan Ayew saw an attempt deflect wide off Leighton Baines before Federico Fernandez's header was cleared off the line by Cenk Tosun from the resulting corner.
Moments later, a smart flick from Jordan Ayew played his brother, Andre, through on goal, but his shot on the stretch was comfortably saved by Jordan Pickford.
For Everton's opener, Lukasz Fabianski had got down well to keep out Yannick Bolasie's half-volley, but his save from Idrissa Gueye's follow-up ricocheted off Naughton's head and bounced over the line before Alfie Mawson could clear - it took a check of the watch to tell referee Lee Mason it was indeed a goal.
Pickford then denied Swansea twice in the opening stages of the second half, first flying to his right to keep out Tom Carroll's header before then standing tall to keep out Andre Ayew's attempt.
Swansea's pressure eventually paid off, for moments after Mawson's header was cleared off the line, Carroll picked out Jordan Ayew out wide, with the striker calmly chesting the ball down before sending a sweet strike beyond Pickford's grasp.
Both sides missed chances to score a winner, with Coleman's close-range effort striking the bar before Abraham fired well over from eight yards out.
Opta stats
- Swansea have only lost one of their last eight Premier League meetings with Everton (W2 D5), with the Swans unbeaten in their last four at Liberty Stadium (W1 D3).
- Swansea City have conceded 13 own goals in the Premier League since 2014-15; five more than any other side.
- Since keeping two clean sheets in December, Everton have conceded in each of their last seven Premier League games on the road.
- Jordan Ayew has scored in three of his last four Premier League games at Liberty Stadium, including of his last two.
Man of the match - Jordan Ayew
After serving a three-match man, Ayew outlined his importance to Swansea with a standout performance at the Liberty Stadium. The 26-year-old linked up well with Carroll and brother Andre, and got the goal he richly deserved with 20 minutes to go.
Jordan Ayew also played four key passes in the match and had another two attempts blocked. On another day, it could have been three or four for Swansea - but it's perhaps typical of their season that they could only score once.
The managers
Swansea boss Carlos Carvalhal: "I think it's very clear [Swansea deserved to win]. The numbers will confirm it - corners, passes, everything. I think we were better in the game. My players did everything.
"I'm doing everything also. With four attackers on the pitch we took risks, but we wanted to win.
"We scored one goal but before and after we could have achieved more. It was important in this game who scored first of course, and before they did we had three or four clear chances."
Everton boss Sam Allardyce: "Even though we were in the lead we had to do a lot of battling today against Swansea, fighting for the three points, because obviously of the position they're in.
"We're the first team to take a point off Swansea in their last five home games, and we knew it was going to be difficult - it was exactly that.
"We didn't make it easy for ourselves because of our poor passing but we got our noses in front. Swansea's pressure eventually told but Pickford made some great saves.
What's next?
Swansea head to Premier League champions-elect Manchester City on Nissan Super Sunday next weekend, live on Sky Sports Premier League from 4pm. Meanwhile, Everton are next in action on Monday Night Football from 7pm against Newcastle on April 23.