Jurgen Klopp’s side fell behind to Son Heung-min’s second-half goal at Anfield before Luis Diaz equalised in the closing stages.
Son tapped in Ryan Sessegnon’s cross in the 56th minute after good work from Harry Kane in the build-up.
Diaz bagged Liverpool’s fortuitous equaliser when his 20-yard drive went in off Rodrigo Bentancur.
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Liverpool, who have already won the League Cup and have Champions League and FA Cup finals to come, moved to the top of the table above Manchester City on goal difference.
But champions City will go three points clear of Liverpool if they beat Newcastle in their game in hand at the Etihad Stadium on Sunday.
That would be a massive boost to City’s hopes of retaining the title with just three games left for both teams after this weekend.
“It is incredibly difficult to play against an opponent with world-class players and a world-class manager when they have had a week to prepare and we play every three days,” Klopp said.
“The dressing room is not flying, come on, but there are other games to play. We just have to keep going.” The draw was also not enough for Tottenham in the race to qualify for next season’s Champions League via a top-four finish.
Tottenham remain fifth and will fall four points adrift of fourth-placed Arsenal if the Gunners beat Leeds.
The remaining Premier League fixtures for City and Liverpool:
Manchester City: Newcastle (home), Wolves (away), West Ham (away), Aston Villa (home)
Liverpool: Aston Villa (away), Southampton (away), Wolves (home)
UNITED COLLAPSE TO NEW LOW
Manchester United have endured a host of humiliations in one of their most embarrassing seasons for decades and their lacklustre loss at Brighton was among the very worst.
Ralf Rangnick’s side were routed by goals from Moises Caicedo, Marc Cucurella, Pascal Gross and Leandro Trossard at the Amex Stadium.
Sixth-placed United are certain to miss the Champions League for only the fifth time in 30 seasons.
With 58 points and only one game left, United’s fifth successive away defeat means they will finish with their lowest points total in the Premier League era.
“It was a terrible performance. From the first until the last minute it was not enough, we can only apologise for this performance and a humiliating defeat,” Rangnick said.
CHELSEA BLOW BIG LEAD IN FRONT OF NEW OWNERS
It was a day of mixed emotions at Stamford Bridge, where Chelsea blew a two-goal lead in a 2-2 draw with Wolves in front of prospective owner Todd Boehly.