Enzo Maresca’s Chelsea took the lead through Enzo Fernandez’s early strike at Stamford Bridge.
Jarell Quansah’s second-half own goal was followed by Virgil van Dijk’s late reply for Liverpool.
Cole Palmer’s stoppage-time penalty condemned the champions to only their third league defeat this season.
While lacklustre Liverpool had little to play for after winning a record-equalling 20th English crown with a 5-1 rout of Tottenham last weekend, Chelsea had every incentive to secure a priceless three points.
Hoping to return to the Champions League via a top-five finish, the Blues sit in fifth place, level on points with fourth-placed Newcastle after their 1-1 draw at Brighton earlier on Sunday.
Sixth-placed Nottingham Forest will join Chelsea and Newcastle on 63 points if they beat Crystal Palace on Monday.
Third-placed Manchester City are only one point clear of Chelsea and, with three games left, the top-five battle is set for a thrilling finale.
Liverpool’s only other league losses in a triumphant campaign came against Nottingham Forest in September and at Fulham in April.
Manchester United are languishing in 15th place following the latest setback in their wretched top-flight campaign.
Ruben Amorim’s side are focused on salvaging their forgettable season by winning the Europa League.
They will host Athletic Bilbao in the semi-final second leg next Thursday, protecting a 3-0 lead, and Amorim made a host of changes, resting Harry Maguire, Bruno Fernandes and Casemiro.
In the 14th minute, Mason Mount scored only his second league goal for United since joining from Chelsea in 2023 as he took Alejandro Garnacho’s pass and slotted home from eight yards.
But Brentford hit back in the 27th minute when United defender Luke Shaw deflected Michael Kayode’s effort into his own net.
United’s leaky defence were punished in the 33rd minute as Kevin Schade headed Christian Norgaard’s cross past Altay Bayindir.
United conceded again when Schade struck with a 70th-minute header.
Yoane Wissa completed the rout four minutes later, poking home for his 18th league goal this season.
Garnacho’s 82nd-minute blast from the edge of the area was followed by Amad Diallo’s stoppage-time effort for the visitors.
But it was little consolation for United, who have lost 12 of Amorim’s 24 league games, winning only six times.
“The players have to understand we cannot do this anymore, we know the context of the season and we need to change that,” Amorim said.
Tottenham are also looking to win the Europa League to paper over the cracks in a miserable campaign.
Ange Postecoglou’s side warmed up for their semi-final second leg against Bodo/Glimt with a 1-1 draw at West Ham.
Tottenham have only one win in their last nine league matches and sit a lowly 16th in the table, leaving them facing their lowest finish since 1976-77.
They are aiming to end their 17-year trophy drought by winning a first European prize since the 1984 Uefa Cup.
But Postecoglou could still be sacked regardless of the Europa League run.
The Australian made eight changes from the 3-1 win in the first leg against Bodo/Glimt to rest his stars for Thursday’s second leg in Norway.
Tottenham took the lead in the 15th minute when Wilson Odobert punished West Ham’s sloppy marking to drill home from Mathys Tel’s pass.
It was Odobert’s first league goal for Tottenham since arriving from Burnley in August.
But Jarrod Bowen levelled for West Ham in the 28th minute, taking Aaron Wan-Bissaka’s pass in stride and shooting through the legs of Tottenham keeper Guglielmo Vicario.
Yankuba Minteh gave Brighton the lead against his former club with a fine finish, curling into the top corner in the 28th minute.
Alexander Isak dragged Newcastle level in the 89th minute, the Sweden striker netting with a penalty for his 23rd league goal this season after Yasin Ayari handled Kieran Trippier’s free-kick. (AFP)
