News that Hull had lost to already relegated Sunderland will have reached the Swansea players before kick-off, and they will have known that if they win out, they will retain Premier League status for next season.
Swansea, who have 35 points, face bottom-of-the-table Sunderland and West Bromwich Albion in their final two games while Hull, on 34 points, play Crystal Palace and finish with a hard game against Tottenham Hotspur.
Swans boss Paul Clement said after his team's crucial 1-0 win over Everton on Saturday: "It is a shame we can't bring all the fans".
"That was the case and it has ended up being a positive weekend". Just look at what happened with Hull, everyone thought it would a home win for them and it did not happen.
He said: "I've been very privileged to have worked with some fantastic teams and different players and got my hands on some unbelievable silverware, but this will be the best because I'm the one making the decisions".
Swansea traveled to Old Trafford to face Manchester United last weekend.
Everton manager Ronald Koeman was happier with his side's second-half display against Swansea City, but acknowledges that they did not create enough to earn a point.
"The players paying for the supporters' tickets came from Leon and I thought it was a brilliant idea", Clement said.
Capitals' stars step up when needed to avoid elimination in Game 5
I was hoping to get some scoring out of Burakovsky; we got that. "My teammates are working hard to help me out", Fleury said. He maintained that as long as he was creating scoring chances, which he was, then he wasn't concerned with his game.
"It gave us a lift before the game knowing that (Hull) result had gone in our favour; we knew if we did something special we could get out of the relegation zone".
Swansea snapped a three-game losing streak by beating Stoke City 2-0 on April 22 and followed that up by snatching an unlikely draw at fifth-placed Manchester United in their last league outing.
Enner Valencia has scored three goals and assisted once in his last seven Premier League substitute appearances for Everton - however, he hasn't scored or assisted in any of his last 10 league starts (four for Everton, six for West Ham).
It proved Everton's last chance, as Swansea held out for the three minutes of injury time - to prompt one of the biggest crowd roars seen at the stadium in recent years.
Second-half goals by Billy Jones and Jermain Defoe earned bottom club Sunderland a first win in 11 games and condemned Hull to a first home defeat under Marco Silva.
"I need to recognise [Swansea] had good defending in the set plays", he told BBC Sport.
There is every chance that the two sides will be locked on the same number of points and relegation could come down to the smallest margins.
But Koeman - who felt more stoppage time than the three minutes allowed should have been played - added: "It was not a disappointing performance".
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