Manchester United’s Eric Bailly scored an own-goal in the 66th minute to give Liverpool hopes of pulling a comeback at Old Trafford, but the Red Devils held on to take all three points thanks to Marcus Rashford’s first half brace.
With the win, Man United went five points clear of third place Liverpool and moved within 13 points of Manchester City.
Liverpool were left to rue a slow start as Rashford twice finished impressively after Romelu Lukaku had outmuscled Dejan Lovren.
The visitors dominated after the break, but could only find a response via a United player when Bailly turned into his own net 24 minutes from time.
Just a second defeat in 21 Premier League games leaves Liverpool still in third, but they could drop to fourth if Tottenham win at Bournemouth on Sunday.
Rashford may not have even have started but for an injury to Paul Pogba suffered in training on Friday.
Without the £89 million ($123 million) French international, Mourinho moved Alexis Sanchez inside behind Lukaku and handed Rashford his first league start of the year on the left.
The Portuguese coach’s plans worked to perfection when Rashford brought the game to life with a superb finish after 14 minutes.