Jurgen Klopp's men sealed a 19th league title for the club with a record seven games left to play after second placed City's defeat left them 23 points adrift.
Liverpool had moved within two points of the title with a 4-0 demolition of Crystal Palace at Anfield on Wednesday.
Their 28th win in 31 league games this season prompted Liverpool star Mohamed Salah to declare "now is our time to win the league" and 24 hours later his wish was granted.
Liverpool got the favour they wanted from Chelsea at Stamford Bridge.
Willian's 78th minute penalty, awarded for a handball by Fernandinho, ended City's two-year reign as champions after Kevin De Bruyne had cancelled out Christian Pulisic's opener.
Liverpool have clinched the title earlier than any other Premier League champions, breaking the previous record of five games left shared by City and Manchester United.
It has been an agonising wait for Liverpool fans across the world, with the coronavirus hiatus forcing them to put the champagne on ice after the Premier League was suspended in March with Klopp's team two wins from the title.
The three-month delay was a final obstacle on Liverpool's long road back to the pinnacle of English football.
Liverpool spent years in the shadow of arch-rivals Manchester United during the Alex Ferguson era before being left behind by the massive spending of Manchester City and Chelsea.
Then managed by Brendan Rodgers, they infamously squandered a golden opportunity to win the title in 2014 when Reds captain Steven Gerrard made his costly slip in a late-season defeat against Chelsea.
But Klopp's team are deserved champions after an incredible campaign that could end in record-breaking style.
Liverpool, who are now one title behind Manchester United's English record haul of 20, are on course to beat Manchester City's record points total of 100 set in 2017/18.
Klopp's men could smash the record for the biggest winning margin, set by City when they finished 19 points clear at the top in that same season.
They are also within touching distance of the most victories in a Premier League season -- 32 by City in 2017/18 and 2018/19.
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