Arne Slot's Liverpool had to hold off a fightback at Anfield from relegation-threatened Wolves, who threatened on Sunday after a brilliant long-range goal from Matheus Cunha.
First-half strikes from Luis Diaz and Mohamed Salah secured the win for Liverpool and ensured they maintained their advantage over second-placed Arsenal.
Liverpool failed to register a single shot on target after the break as Wolves dominated the chances.
Diaz bundled the ball over the line from close range in the 15th minute to give the home team the lead, before Salah doubled the advantage from the penalty spot in the 37th after Diaz was brought down.
It was the Egypt international's 28th goal of an outstanding season.
But if the home crowd was expecting a routine victory against Wolves, it was anything but.
Cunha's drag-back and curled finish from around 20 metres in the 67th minute came after a sustained period of pressure from the visitors.
Before that, Marshall Munetsi was denied when through on goal — it took a crucial block in front of goal from Jarell Quansah to prevent him from converting late on.
At the Tottenham Hotspur Stadium, James Maddison's 13th-minute goal secured Spurs their much-needed win over United in the battle of the Premier League's 'crisis clubs'.
The two teams started the day closer to the relegation zone than the top-four and it was Spurs who gained three points following an early effort by the fit-again Maddison.
Maddison celebrated with a shush to the camera after midweek criticism from ex-Man United captain Roy Keane and this first home league win for Tottenham since November 3 moved the hosts up to 12th in the table.
Spurs fans had protested against chairman Daniel Levy and majority owners ENIC earlier in the day, but come full-time it was injury-hit United and boss Ruben Amorim who were left to reflect on where to go next following another league defeat.
With PA
