Marouane Fellaini opened the scoring just before half time, before Chris Smalling added a second just shy of the hour mark.
Goals from Henrikh Mkhitaryan and Bastian Schweinsteiger then completed the victory as the holders booked their place in the fifth round of the competition.
4 - Man Utd have scored 4+ goals in a game 6 times under Mourinho (36 games), two more than they did in 103 games under van Gaal. Exciting.— OptaJoe (@OptaJoe) January 29, 2017
The win means that United have now scored four or more goals six times under Jose Mourinho in 36 games, two more than they managed in 103 games under previous boss Louis van Gaal.
Mourinho’s men also hit four in the last round of the competition, seeing off Reading 4-0 thanks to goals from Wayne Rooney, Anthony Martial and a double from Marcus Rashford.
The Red Devils have now scored four goals in consecutive rounds of the FA Cup for the first time since 2009 (when they beat Derby 4-1 and Fulham 4-0).
This is also the first time the Red Devils have scored four or more in successive rounds at Old Trafford since 2003 (when they beat Portsmouth 4-1 and West Ham 6-0 West Ham).