Roberto Firmino’s late winner against Wolves took Liverpool 16 points clear at the top of the table with a 14th consecutive Premier League victory.
Jordan Henderson gave the Reds the lead from Trent Alexander-Arnold’s corner.
Raul Jimenez headed Wolves level from Adama Traore’s cross – the first league goal Liverpool have conceded in 50 days.
Wolves dominated the second half but Firmino popped up to fire in a winner from Henderson’s pass.
The Reds, who lost Sadio Mane to a first-half injury, are only the third team to go 40 games unbeaten in the Premier League.