Home fans were gearing up to taunt their biggest rivals on Sunday as Arne Slot's side were just 10 minutes away from going eight points clear of Arsenal at the top with a match in hand.
But Amad Diallo stabbed home Alejandro Garnacho's cross - adding to Lisandro Martinez's first goal in two years - in the 80th minute to earn them a point, after United had conceded a lead to trail 2-1 when Cody Gakpo and Mohamed Salah's penalty turned things around.
Liverpool's Mohamed Salah celebrates scoring their second goal from the penalty spot. (AP PHOTO)
The performance would have cheered Amorim, who had called for the leaders in the squad to step up after five defeats in his first eight matches in charge.
It was no surprise they did it against Liverpool, who remain favourites to equal the Red Devils' 20 league titles despite dropping two points at home, as the rivalry between England's two most successful clubs always raises the stakes.
And while it may have brought the best out of United from a resilience point of view, it strangely did not seem to have the same effect on the hosts, who were slow off the mark in a game only given the go-ahead at midday after heavy snow on Merseyside.
But quality endures and after a lacklustre first half Liverpool stepped things up after Martinez's fierce angled strike beat Alisson Becker and went in off the crossbar.
It was exemplified first by Gakpo, who scored his 10th goal in his last 15 appearances by cutting in on his right foot - sending Matthijs de Ligt sliding off the pitch - to smash a shot past Andre Onana.
But the coup de grace seemed to have been applied by Salah, whose 18th goal of the season saw him draw level with Thierry Henry in joint-seventh place on the all-time Premier League goalscorers chart with 175 goals.
Mac Allister's header from Trent Alexander-Arnold's cross hit De Ligt's raised left arm and although referee Michael Oliver played on he was informed by VAR he should view the monitor and he subsequently changed his mind.
Onana, who had engaged in some pre-penalty shenanigans with a number of Liverpool players, guessed the right way but Salah's shot was too powerful for him.
Usually, that would be that - especially against a United side who had lost their last three league games without scoring - but Diallo nipped in front of Andy Robertson to snatch a point.
In another dramatic match earlier on Sunday, Raul Jimenez scored a 91st-minute penalty to salvage a 2-2 draw for Fulham at home to Ipswich.
It was Jimenez's second penalty of the match as Fulham twice came from a goal down at Craven Cottage.
Relegation-fighting Ipswich went ahead through Sam Szmodics in the 38th and Jimenez levelled from the spot in the 69th.
Ipswich went in front again through Liam Delap's penalty in the 71st and looked like climbing out of the relegation zone.
But when Jimenez was brought down by Leif Davis in the box, referee Darren Bond pointed to the spot again and Jimenez made no mistake.
Fulham are now ninth, while Ipswich are 18th and below Wolves on goal difference, having played a game more.
With AP
