The drama wasn’t over yet. A minute later, Palmer’s effort from outside the box was deflected past Andre Onana to seal a spectacular comeback.
It doesn’t get any easier for Erik ten Hag’s team, who host Liverpool at Old Trafford on Monday.
English football’s biggest rivalry resumes with Liverpool chasing the title and United on the slide.
A 12th league defeat of the campaign for United was played out in front of new co-owner Jim Ratcliffe at Stamford Bridge and will likely see pressure intensify on manager Ten Hag.
Liverpool beat Sheffield United to move top again
Alexis Mac Allister scored a stunning goal to help Liverpool beat Sheffield United 3-1 and return to the top of the Premier League.
Darwin Nunez had given Jurgen Klopp’s team a first-half lead at Anfield, but Sheffield United were gifted a way back into the game through Conor Bradley’s own goal after the break.
With Liverpool in danger of dropping points in the race for the title, Mac Allister eased the tension when he blasted a long-range effort into the top corner in the 76th minute.
The game was put beyond doubt when substitute Cody Gakpo headed in a third in the 90th.
Liverpool moved two points clear of Arsenal at the top, but they had to dig deep against last-place Sheffield United.
The Merseyside club needed a touch of fortune to take the lead in the 17th after Sheffield goalkeeper Ivo Grbic’s attempted clearance was blocked by the jump of Nunez.
The forward had his back to the ball, but it ricocheted off him and past Grbic before rolling into the empty net.
After the break, the visitors were given an unexpected route back when Bradley diverted Gustavo Hamer’s header into his own net in the 58th minute.
But Mac Allister swung the match in Liverpool’s favour with his lashed effort and he could have added another when he hit the bar with a free kick late on before Gakpo’s header.
EPL ladder
(Team, points)
1. Liverpool 70
2. Arsenal 68
3. Man City 67
4. Aston Villa 59
5. Tottenham 57
6. Man United 48
7. West Ham 45
8. Newcastle 44
9. Brighton 43
10. Chelsea 43
11. Wolves 42
12. Bournemouth 41
13. Fulham 39
14. Crystal Palace 30
15. Brentford 28
16. Everton 26
17. Nottingham Forest 25
18. Luton Town 22
19. Burnley 19
20. Sheffield United 15
- with AP