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Liverpool have 94 points and Manchester City 92 but Pep Guardiola's City have two games remaining, including Monday's home match with Leicester City.
Antonio marked his winner with an exuberant goal celebration and said he was delighted to become the first opposition player to score in the new stadium.
The victory was an important one for Tottenham, who face a daunting trip to league leaders Manchester City in the Champions League on Wednesday.
Huddersfield Town were relegated while Manchester United celebrated the full-time managerial appointment of Ole Gunnar Solskjaer with a 2-1 win over Watford.
Tottenham Hotspur's challenge faltered again with a 2-1 loss at Southampton.
City, who beat Bournemouth 1-0 on Saturday, have 71 points while Liverpool have 70 after their fourth draw in their last six games.
The Premier League battle appears a two-horse race after leaders Liverpool and Manchester City both won on Wednesday while Tottenham fell to a second straight defeat.
Visitors Chelsea desperately needed a response after back-to-back humiliating away losses, with last Sunday's 6-0 thrashing by Manchester City following a 4-0 reverse at Bournemouth.
The win moves Juergen Klopp's side three points above second-placed Manchester City.
Aymeric Laporte headed the opener against Everton just before the interval and substitute Gabriel Jesus sealed the victory deep in stoppage time for City, who returned to the league's summit for the first time since December 8.