Jurgen Klopp's side went in front through Sadio Mane at London Stadium on Monday, although the goal should have been disallowed for a clear offside in the build-up.
But Antonio quickly levelled for the Hammers, with his fourth career goal against Liverpool leaving the league leaders just three points clear of chasing City, who had defeated Arsenal 3-1 the previous day.
And the result could have been even worse for the Reds, Declan Rice wasting a free header shortly before the interval, although substitute Divock Origi almost won it in added time.
A N T O N I O O O O pic.twitter.com/rpguAgOggf— West Ham United (@WestHamUtd) February 4, 2019
Javier Hernandez wasted two good early chances as Liverpool started poorly, but they took the lead in controversial circumstances in the 22nd minute.
Brilliant skill from Adam Lallana found James Milner, who cut the ball back for Mane to finish well, but replays showed the makeshift right-back was offside when he received the pass.
West Ham equalised within six minutes, though. Felipe Anderson caught out the Liverpool defence with a smartly taken free-kick, sliding a low pass into the right channel for Antonio, who shrugged off Naby Keita and drilled a fine finish across Alisson and in off the post.
Rice and Issa Diop missed headed chances either side of half-time as Liverpool continued to defend set pieces poorly, while Mohamed Salah could not make the most of two second-half openings he created for himself.
Hammers captain Mark Noble almost snatched all three points, his 73rd-minute drive flying narrowly over Alisson's goal.
But Origi could have settled matters in the 94th minute, the Belgian - a late hero against Everton at Anfield earlier in the campaign - firing straight at Lukasz Fabianski after Keita picked him out with a chipped pass, the flag staying down again despite the striker b offside position.
4 - Michail Antonio has scored four goals in his five Premier League games against Liverpool, more than he has managed against any other side. Familiar. pic.twitter.com/4wt5r8quFu— OptaJoe (@OptaJoe) February 4, 2019
What does it mean? Liverpool feel the heat
West Ham's inconsistency meant it was hard to guess what Hammers side Liverpool would face, yet it was the Reds - shorn of injured midfield metronome Jordan Henderson - who struggled for fluency in an open game. City will go top if they win a rearranged fixture away at Everton on Wednesday.
Inventive Felipe Anderson shines again
With talismanic striker Marko Arnautovic ruled out through injury, West Ham relied even more than usual on Felipe Anderson, the club's record signing, to provide a spark. The Brazilian duly stepped up, too. He was a constant menace and it was his clever quick free-kick that created Antonio's equalising goal.
Keita concentration lacking
A constant feature of the game was Keita losing his man at set-piece situations. Antonio rolled the Liverpool midfielder far too easily for his goal, while Keita was often lax on and off the ball as well.
Key Opta facts
- West Ham are unbeaten in three consecutive home Premier League games (W1 D2) for the first time since February 2018 (a run of four games)
- Liverpool have won 62 points from their opening 25 Premier League games this season - only during the 1987-88 campaign have they had more points at this stage of a top-flight season (63).
- Sadio Mane has scored three goals in his last three Premier League appearances - he had scored just two in his previous 11.
- James Milner has registered 81 assists in the Premier League, one more than David Beckham (80).
- Naby Keita has made more Premier League appearances without losing a game than any other player in the competition's history (18 games, 14 wins, 4 draws).
Liverpool will look to bounce back at home to Bournemouth on Saturday after back-to-back 1-1 draws. West Ham, meanwhile, go to Crystal Palace on the same day.