French midfielder Paul Pogba scored twice with Anthony Martial also on target as United made it 10 wins and a draw in the 11 matches since Ole Gunnar Solskjaer became interim manager after Jose Mourinho’s sacking.
The win lifted United into fourth spot with 51 points and they will stay there if Chelsea lose to City.
Cardiff City ended another traumatic week by securing a vital 2-1 victory at fellow strugglers Southampton.
Days after it was confirmed that the body of Emiliano Sala, the club’s new signing from Nantes, had been recovered from a plane that vanished over the English Channel, Cardiff were boosted by Kenneth Zohore’s last-gasp winner which lifted the Welsh club out of the bottom three.
Arsenal maintained their top-four push with a 2-1 victory at rock-bottom Huddersfield Town, their first away win in the league since November secured by goals from Alex Iwobi and Alexandre Lacazette.
The problems mounted for Everton manager Marco Silva as his side went down 1-0 to his old club Watford at Vicarage Road and had defender Kurt Zouma sent off in stoppage time.
Wilfried Zaha earned Crystal Palace a 1-1 draw at home to West Ham United who had led through Mark Noble’s penalty.
In the day’s late game, Burnley continued their unbeaten league run in 2019 with a 3-1 victory at Brighton & Hove Albion, moving them three points clear of the bottom three and ensuring Southampton will finish the weekend in the relegation zone.
Poor performances in draws against Leicester and West Ham, results which allowed City to eradicate their lead, had raised questions about Liverpool’s nerve as they chase a first English title since 1990.
Had their keeper Alisson Becker not parried out Ryan Fraser’s shot in the second minute, it could have been a fraught afternoon in the Anfield sunshine.
But once Mane headed his side in front Liverpool assumed control. Wijnaldum’s deft lob over Artur Boruc doubled their lead and Salah got in on the act after good link-up play with Roberto Firmino.
Salah also struck the crossbar as Liverpool confirmed their return to form. They moved to 65 points from 26 matches with City on 62 and Tottenham Hotspur, who host Leicester on Sunday, a little further back on 57 points.
«We were not happy with the performances from the previous two games and struggled a bit with set-pieces,» Klopp said.
«There were a lot of things we had to improve. We have high expectations and today we won in an impressive manner — we had some outstanding performances on the pitch.
«We wanted to show a reaction. It’s our job not only to come through but to really perform and convince.»
United’s extraordinary resurgence under Solskjaer has seen them collect 25 points from his nine league games — more than any other manager has achieved in his first nine matches in charge of a single club in the competition.
World Cup winner Pogba was again the architect of the victory as he took his tally of league goals to seven since former striker Solskjaer arrived.
«Ole helps every player play at their best. Ole is himself. He’s not acting and he’s given joy and confidence to everyone,» Pogba said.