Jurgen Klopp’s side had struggled for goals heading into the match but took the lead with a fine Mohamed Salah finish, only for United to turn the match around with goals from Mason Greenwood and Marcus Rashford – each forward setting the other up, either side of half-time.
Liverpool then forced further chances and after James Milner fired over, the No. 7 cleverly dummied to let Salah through to bury his second.
The away team remained in the ascendancy, but it was United who found a third goal as sub Bruno Fernandes curled in a free-kick to send his side through 3-2.
Here are five things we took from the cup clash at Old Trafford.
Table-topping Manchester United could hardly be in better form, given improved home form in the league and recently avoiding defeat at Anfield.
Now they might just be thinking about a domestic double.
The back-and-forth nature of this clash could have fallen either way, but the clinical edge fell the way of Ole Gunnar Solskjaer’s side to send them into the fifth round.
Big sides still remain involved – Leicester and Man City have equally good form and Spurs are tough to match over 90 minutes – but positivity is rife at Old Trafford right now.
It has been chop-and-change for United in the wide areas of the attack recently, but with Rashford restored to the left side and producing a very accomplished showing, it might be a while before they switch matters up.
Luke Shaw has been excellent at left-back recently and he and Rashford showed a great understanding and link-up many times over during the 90 minutes, with the bulk of the home team’s chances coming from that flank.
The big loser there might be Anthony Martial, considering Edinson Cavani’s impact in the No. 9 role of late.
Salah back on the scoresheet
They ended up on the wrong side of the result, but a big positive for the Reds on the day was the return to scoring form of Mohamed Salah.
The Egyptian netted his brace with a clinical pair of finishes inside the box, one right foot and one left, giving reason to feel that there’s momentum to be gained despite the cup exit.
It’s four games without a goal in league play for the Reds, so this improved game in an attacking sense has to be taken forward to the game against Spurs on Thursday.
After recent struggles to create clear openings, Jurgen Klopp switched up the team shape on Sunday to go with two at centre-forward and two, Curtis Jones and Gini Wijnaldum, playing as narrow attacking options from the sides of midfield.
It was still very fluid and often left the Reds with a three-man midfield, and they reverted to a three later in the half, but initially in particular there was more emphasis on a central press with Salah in alongside Firmino.
That was a positive going forward, but it was an issue at the back – with United able to overload and exploit their left, Liverpool’s right, when Shaw got forward and Marcus Rashford went one-on-one with Rhys Williams.
United already know they’ll be playing at home to West Ham United in the next round.
That means a return to Old Trafford for David Moyes, an intriguing match-up given the Hammers boss is probably in his most positive and productive moment as a manager since he was initially appointed as Manchester United boss.
Two in-form teams with their eyes on long-overdue silverware to meet, then, with a quarter-final place at stake – when the prospect of Wembley and glory can feel tantalisingly close.