Under-strength Chelsea cut the gap at the top to two points with two games to play in a tactical triumph for their manager Jose Mourinho.
The result boosted the title aspirations of third-placed Manchester City, who can close the gap on the leaders to three points if they beat Crystal Palace in Sunday’s late match.
City will also have a game in hand and a better goal difference than their rivals.
But Mourinho ruled Chelsea out of contention, telling Sky Sports; “the Champions will be City or Liverpool.”
Whether or not that the case, Chelsea will have beaten both of their rivals at home and away.
Liverpool lost 2-1 at Stamford Bridge in December and had not been beaten since until Sunday.
Chelsea also won at City in February, having beaten them at home four months earlier.
Missing five leading players through injury and suspension, Mourinho also chose to rest others ahead of Wednesday’s Champions League semi-final second leg at home to Atletico Madrid.
Liverpool manager Brendan Rodgers, who once worked at Chelsea under Mourinho, accused his former club of playing defensively and having “two buses parked” in front of their goal.
But his side, who had won their previous 11 games to become favourites for the title, failed to make enough chances on the day.
Philippe Coutinho wasted an early opportunity and Mamadou Sakho also missed the target but Chelsea’s reserve goalkeeper Mark Schwarzer did not have a shot to save for almost an hour.
Just before the interval Liverpool captain Steven Gerrard slipped and fell as he received a square pass near the halfway line and Demba Ba ran on to finish coolly.
Schwarzer, standing in for the injured Petr Cech, did well to keep out Joe Allen’s volley and pushed over a shot from Luis Suarez.
But the Uruguayan striker, favourite to be named Player of the Year by his fellow professionals later on Sunday, was generally well controlled by a solid Chelsea defence and although the London side were pushed back for much of the second half, they still counter-attacked dangerously at times.
Goalkeeper Simon Mignolet had to save low down from Andre Schuerrle on one such break and in added time Fernando Torres, once a Liverpool hero, set up the Brazilian midfielder Willian to score the second goal and clinch victory.
Chelsea were left to rue a shock home defeat by Sunderland in their last game, which was the first time Mourinho had lost in 78 league matches at Stamford Bridge.
Had they won that game as expected they would now have been top of the table and would have the title in their own hands.
They still need one more point to guarantee finishing in the top three and earn automatic qualification for next season’s Champions League.
Chelsea’s remaining fixtures are against two relegation candidates, Norwich at home and Cardiff away.
Liverpool play away to Crystal Palace and finish at home to Newcastle, hoping that City will have dropped points. The Manchester club’s last three games are away to Everton next Saturday, then home to Aston Villa and West Ham in the final week of what has been a topsy-turvy Premier League season.
Rodgers refused to concede anything, telling Sky Sports: “Manchester City have still got the games to play. We’ll fight to finish as high as we can and see where it takes us.”
(Writing by Steve Tongue, editing by Ed Osmond)