Manchester City swept back to the top of the table with a stylish 2-0 win at Fulham, while Huddersfield equalled the record for the earliest Premier League relegation after defeat at Crystal Palace on Saturday.
Amid the drama at the top and bottom, Manchester United celebrated Ole Gunnar Solskjaer's first match as permanent manager with a 2-1 win over Watford to climb into fourth place.
Bernardo Silva's fifth-minute strike from the edge of the area was followed by Sergio Aguero's cool finish as City effectively wrapped up the points in the first 27 minutes.
City lead Liverpool by one point with seven games remaining for both sides, but Jurgen Klopp's men can regain pole position with victory over third-placed Tottenham at Anfield on Sunday.
Pep Guardiola's side remain on course for an unprecedented quadruple of Premier League, Champions League, FA Cup and League Cup, which they retained last month.
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A potential 14 games now stand between them and history, but there will be far tougher tests in wait than struggling Fulham, who are 16 points adrift of safety with just six games left.
"The way we started was amazing. They surprised me again, the first 15-20 minutes was exceptional," Guardiola said.
"Every game we have to win if we want to be champions. We have tough opponents, but that is the challenge."
Bottom-of-the-table Huddersfield's two-season stay in the top flight came to an end at Selhurst Park as they slumped to a 24th defeat in 32 league games by losing 2-0 at Palace.
Huddersfield are only the second club to be relegated from the Premier League in March after Derby went down with 11 points in 2008.
They survived just one day longer than Derby in 2008 and equalled their unwanted Premier League record of relegation after 32 games.
Already destined for the drop, Jan Siewert's side had their fate sealed due to their result and wins for Burnley and Southampton.
Luka Milivojevic's 76th-minute penalty put Huddersfield behind after a foul on Palace winger Wilfried Zaha.
Patrick van Aanholt's 88th-minute strike pushed the bedraggled Terriers back to the Championship.
"It is hard to say what I am feeling, disappointment of course. It sums the season up that a penalty decides the direction. I haven't counted but we've conceded maybe eight to 10 penalties this season," Siewert said.
"For me, in life, there is failure and success and it belongs together.
"I don't want to talk about those failures publicly, but it is important to learn as a club and this club is willing to do it."
- Lethal United -
At Old Trafford, Solskjaer received a rapturous reception from the crowd when he strolled down the touchline just before kick-off, days after agreeing a three-year contract following his successful spell as interim boss.
After Watford dominated the early stages, Solskjaer was applauding a lethal United counter-attack to open the scoring through Marcus Rashford in the 28th minute.
Luke Shaw unfurled a superb pass from deep in his own half and Rashford sprinted clear to clip a deft finish over Watford keeper Ben Foster for his 13th goal of the season.
After successive defeats against Arsenal and Wolves before the international break, Anthony Martial ensured United got back on track when he bundled home in the 72nd minute despite Watford's appeals for offside.
It is the first time since the 1995-96 season that United have had four players score 10 or more goals in a Premier League campaign as Martial joined Rashford, Romelu Lukaku and Paul Pogba in double figures.
Abdoulaye Doucoure scored for Watford in the 90th minute, but United are level on points with Tottenham and one point above fifth-placed Arsenal, who host Newcastle on Monday.
At Turf Moor, Burnley moved five points clear of the relegation zone with a 2-0 victory over Wolves.
Sean Dyche's side took the lead in the second minute when Chris Wood's shot hit a post and deflected off Conor Coady for the Wolves' defender's third own goal this season.
Dwight McNeil netted in the 77th minute to improve Burnley's chances of survival.
Southampton also took a step towards beating the drop with a 1-0 win over south-coast rivals Brighton.
Pierre-Emile Hojbjerg chipped in from Nathan Redmond's pass in the 53rd minute to leave Saints five points clear of third-bottom Cardiff, who face Chelsea on Sunday.
Leicester beat Bournemouth 2-0 with goals from Wes Morgan and Jamie Vardy, while Everton won 2-0 at West Ham thanks to strikes from Kurt Zouma and Brazilian Bernard.