United came into the fixture knowing they had lost their previous four FA Cup meetings against Chelsea, including last season’s final at Wembley, and also saw their unbeaten record under Ole Gunnar Solskjaer ended by Paris Saint-Germain in the Champions League last week.
However, they enjoyed an impressive first half and went into the break with what turned out to be an unassailable two-goal lead thanks to respective headers from Ander Herrera and Paul Pogba.
Chelsea tried to put United under the cosh throughout the second half, but never really looked like preventing the Red Devils from booking their place in the quarter-finals as the pressure continues to mount on Blues boss Maurizio Sarri.
Chelsea boasted five changes from the Europa League win against Malmo on Thursday as Antonio Rudiger, N'Golo Kante, Marcos Alonso, Eden Hazard and Gonzaolo Higuain replaced Andreas Christensen, Emerson, Ross Barkley, Olivier Giroud and Willian.
Sergio Romero, Chris Smalling, Juan Mata and Romelu Lukaku came in for David De Gea, Eric Bailly, Jesse Lingard and Anthony Martial in four changes to the Manchester United side which lost 2-0 to PSG in Europe.
United just about edged the opening 10 minutes, but Chelsea had the first effort of note in the 12th minute when David Luiz’s 25-yard free-kick was palmed away by Romero and Pedro’s follow-up attempt was well blocked before United’s custodian managed to gather.
Moments later Hazard flashed a curling effort just wide of the United goal, before the visitors had their first serious attempt on target with Herrera’s fierce effort on 15 minutes parried away by the diving Kepa Arrizabalaga.
On 18 minutes Cesar Azpilicueta put a cross into the area and Higuain sent a glancing header wide when he should have at least hit the target.
However, it was United who drew first blood just after the half-hour mark when Mata played the ball out wide to Pogba who lifted an inch-perfect cross onto the head of Herrara and the Spaniard guided his downward header into the bottom corner of Kepa’s goal.
Chelsea looked to respond in the remainder of the half, but it was United who grabbed the second goal of the evening on the stroke of half-time when Marcos Rashford’s cross from the right dropped perfectly to Pogba and his header beat Kepa from 10 yards.
United were fortunate not to be reduced to ten men on 52 minutes when Nemanja Matic fouled Kante in the middle of the pitch, but referee Kevin Friend was lenient in not producing a second yellow card of the evening to the Serbian.
Chelsea continued to press in search of an equaliser and it took an excellent block from Luke Shaw to prevent Pedro getting a chance to score after he was played in down the right of the United box by Kante on 56 minutes.
Shaw collided with Romero during the challenge and both required treatment before being able to continue.
On 65 minutes Hazard cut inside the area from the right channel and looked a certainty to hit the target, only for Victor Lindelof to get enough of a block on the shot to divert the ball over his own crossbar.