First-half goals from Sadio Mane and Georginio Wijnaldum together with Mohamed Salah’s 48th-minute effort saw Liverpool to a 3-0 win over Bournemouth at Anfield.
Victory meant Liverpool, who had been second on goal difference, leapfrogged Manchester City by three points ahead of the reigning champions’ match at home to Chelsea on Sunday.
Meanwhile United’s revival under caretaker manager Ole Gunnar Solskjaer continued with an equally comfortable 3-0 win away to Fulham.
Liverpool had dropped points in successive 1-1 draws against Leicester and West Ham, sparking suggestions they were losing their nerve in a quest to end the club’s 29-year wait to be crowned champions of England once again.
Mane, however, eased the pressure with an early headed goal at Anfield.
Liverpool doubled their lead through Wijnaldum’s 34th-minute lob before Salah’s curling shot sealed victory.
“We knew we were not happy with our performance in the last two or three games,” said Liverpool manager Jurgen Klopp. “We want to play convincing football we want to perform.”
In London, Paul Pogba scored two goals — including a second-half penalty — either side of an Anthony Martial strike as United made it 10 wins in 11 game since former striker Solskjaer was put in temporary command.
Chelsea could regain a spot among the Champions League qualifying places against Manchester City.But United, 11 points adrift of the top four when Jose Mourinho was sacked in December, are back in the hunt now.
“There are so many games left, but we hope to stay in the top four,” said Solskjaer.
Arsenal inflicted more misery on Huddersfield with a 2-1 win away to the bottom-of-the-table club.
Alex Iwobi and Alexandre Lacazette put Arsenal 2-0 up before half-time, with Sead Kolasinac’s own-goal too late for the Terriers.
Elsewhere under-pressure Everton manager Marco Silva’s return to Watford ended in a 1-0 defeat thanks to an Andre Gray goal.
Everton’s loss was compounded when Kurt Zouma was sent off after the final whistle for complaining to referee Lee Probert.