Everton are in the hunt for European football next season and can leapfrog fifth-placed Arsenal with a win at Swansea City, thereby strengthening their position before they meet the Gunners in north London.
The home side then blew a chance to double the lead when Ki Sung-Yueng’s miscued shot fell into the path of Ayew, who with Stekelnburg stranded, could only slice his volley against the outside of the post.
Swansea have one more point than Hull ahead of their final games, away to Sunderland next Saturday and at home to West Brom on the last day of the season.
‘The diamond of Swansea meant we brought Gareth (Barry) in.
The lead was nearly doubled four minutes later as Sigurdsson’s centre found Alfie Mawson and the goal-scoring defender was only foiled by a desperate block from Mason Holgate.
The Toffees haven’t lost an away Premier League game against a side occupying the relegation zone since November 2012, a 2-1 defeat at Reading.
I was fighting relegation in Spain with Athletic Bilbao and it’s very hard being in this position, but I think we have a good dressing room.
Everton, without a win in three games overall, return to action next weekend with a home match against Watford.
Worse still, the Everton has failed to score on five separate occasions at home, and the club will be hoping that their attacking juggernaut Romelu Lukaku will rediscover his shooting boots, when the side locks horns with Swansea AFC this Saturday.
Substitute Leroy Fer almost scored moments after coming onto the pitch, he got onto Olsson’s cross and hit his shot first-time but Maarten Stekelenburg was on-hand to make a stunning save to keep Everton in the game.
With an arm draped around one of his players, Swansea manager Paul Clement walked toward the team’s celebrating fans and held up two of his fingers.
‘I have been with Real Madrid when there has been 85,000 there, and it is not as loud as that (the Liberty Stadium) because they tend to sit and watch, ‘ Clement said. Mawson looked like a brick wall at times.
But then it was Swansea who missed two big chances to make the game safe, as Sigurdsson’s corner found Federico Fernandez, whose goal bound header bounced over via the shoulder of Barkley. Easier said than done, but at least their safety is in their own hands.