United gave goalkeeper Dean Henderson, Victor Lindelof, Donny Van de Beek and Marcus Rashford among others a start, while Mohamed Salah and Roberto Firmino were recalled by Jurgen Klopp.
The Premier League champions hit the front on 18 minutes after Salah ran on the shoulder of the defensive area following a ball from Firmino to lob over Henderson.
However, it didn't last long as United levelled when Mason Greenwood drilled a long ball from out wide by Rashford into the bottom-corner.
United had a tail up their sleeves following the equaliser, and could've gone in front ten minutes before halftime from a corner-kick by Luke Shaw, but Scott McTominay headed over goal.
Following a strong end to the first half, United were fired up for the second half and duly went ahead on 48 minutes through a composed one-on-one finish from Rashford.
Liverpool responded after ten minutes as a teasing ball into the centre of the area from Firmino allowed Salah to fire in a first-time strike from close-range.
This fired up the Reds seconds later after a mazy run towards the area from Trent Alexander-Arnold culminated with a fiery shot which Henderson turned behind for a corner.
United looked to regain momentum on 66 minutes and a double change saw Bruno Fernandes replace Van de Beek and Fred enter for Mason Greenwood.
Salah came close to a hat-trick a little later after running onto a ball into space to go clear on goal, but Henderson went down to parry.
The Red Devils reclaimed advantage towards the last 12 minutes when Fernandes sent a low free-kick from outside the area into the bottom-corner.
It could've been four from a header in the area by Edinson Cavani two minutes from time following a cross from the right, but the post rescued the Reds as United marched onto the fifth round.
