Everton kept alive their hopes of playing in Europe next season after a 48th-minute header from Brazilian forward Richarlison gave them a 1-0 Premier League win at home against Wolverhampton Wanderers on Wednesday.
The result lifted Everton to eighth place on 59 points before the last round of games, level with sixth-placed Tottenham Hotspur and seventh-placed West Ham United, who were at relegated West Bromwich Albion in a later kickoff.
Everton manager Carlo Ancelotti was hopeful his side could spring an upset on the final day of the season after a topsy-turvy campaign.
"We are in the fight, nothing is impossible," the Italian told Sky Sports. "Manchester City will be the most difficult game but it was important to stay there.
"They are the best team in Europe but we have to try. To qualify for Europe it will be a fantastic season. If we don't qualify it will be a good season."
Everton snapped a five-game winless home streak as Richarlison rose superbly in the heart of the penalty box to meet an outswinging Gylfi Sigurdsson corner and leave visiting goalkeeper John Ruddy clutching thin air.
But Everton improved in the second half after Richarlison struck and Ruddy did well to deny Dominic Calvert-Lewin in the 71st minute before Sigurdsson twice went close with long-range efforts.
The home side withstood some late pressure from Wolves and threatened to add a second on the beak as Calvert-Lewin failed to connect with Richarlison's cross from the left.
Everton's Seamus Coleman lauded the home supporters as a factor after the Toffees had suffered a record-equalling nine league defeats at home in a top-flight season.
"We can't underestimate the difference the fans made today," he said.
"We've been crying out for it all season. It's no excuse for our home form but it is just so great to see fans back. It makes a difference to our performances, without a shadow of a doubt."