Swansea had scored only once in the three games top scorer Ayew had sat out following his red card at Huddersfield last month.
Results elsewhere mean Swansea are now five points clear of the drop - despite being placed 17th - as they head into a hard run of fixtures, but remember they still have to play two of the teams below them in Stoke City and Southampton.
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That defeat came in between two losses to Liverpool as they were knocked out of the Champions League at the quarter-final stage. We always gave them the opportunity to be solid, compact in the low block with strong physical players.
However, Swansea, now with 33 points from as many games, are five points clear of third-bottom Southampton - with five games left of the 2017-18 English top-flight season.
The Toffees, meanwhile, are looking to bounce back from disappointing results against Manchester City and bitter rivals Liverpool, and will look to make it successive victories on the road for the first time since September 2016 after they saw off struggling Stoke City 2-1 before the match global break.
Returning from a three-match ban, Ayew struck his 11th goal of the season in the 71st minute just when Everton appeared on course for a win at Liberty Stadium. "I'm sure Swansea are saying they should have won it and perhaps they should but our keeper takes some beating".
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It's somewhat unclear as to what is covered under the memo's mention of an Apple Watch Series 2 not powering on. Eligible devices are any 42mm Series 2 Apple Watch models in the Sport, Nike+, Hermès, and Edition lines.
'It was one of our best performances of the season, but in football you can't get everything'.
And the travelling fans rounded on Allardyce both at half-time and when he replaced winger Yannick Bolasie with central defender Ramiro Funes Mori in the final quarter. "But we would still like to have performed better".
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Rookie Jack Roslovic, replacing injured veteran Mathieu Perreault, had two assists in the game that ended with a series of fights. That's why you had to feel good for them this year - as they returned one of the great playoff traditions: the Winnipeg whiteout.