The Blues warmed-up for Monday night's FA Cup quarter-final replay against Tottenham at White Hart Lane with an easy win - courtesy of goals from Andriy Shevchenko, Salomon Kalou and substitute Michael Ballack.
Struggling United were also hit by the loss of striker Rob Hulse who was taken to hospital with a suspected broken leg.
It was Chelsea's sixth successive victory in the Premiership since their defeat against Liverpool in January and their sixth clean sheet.
The success keeps them six points behind the leaders at the Premiership summit and the result was never in doubt after Andriy Shevchenko put them in front after just three minutes.
The goal owed much to the power and vision of Chelsea centre-half Ricardo Carvalho who won the ball in his own half and burst through the middle before delivering a pin-point pass to the Ukraine striker on the edge of the United penalty area.
Shevchenko, often criticised for his lack of ball control this season, brought down Carvalho's pass with his right thigh and then despatched a glorious left-foot volley into the roof of the net.
The champions increased their advantage in the 16th minute when a cross from Shaun Wright-Phillips caused panic in the United defence.
The lurking Shevchenko helped the ball on and Salomon Kalou scored his second goal in three games with a simple tap-in.
But two minutes later United gave Chelsea goalkeeper Petr Cech something to do when Colin Kazim-Richards unleashed a 25-yard drive that forced Czech international to punch clear.
United striker Rob Hulse tried his luck second later when he produced an ambitious overhead kick from a cross by Keith Gillespie, but his effort trickled wide of Cech's right-hand upright.
However, it was his last contribution as the striker was carried off with a suspected broken leg which he sustained when attempting to get on the end of cross from Gillespie.
It could have been even worse for United, in terms of the scoreline, in the 31st minute when a cross from Arjen Robben eluded their defence.
However, Shevchenko's goalbound shot was cleared off the line by Chris Armstrong.
United felt harshly treated moments later when they had a Claude Davis goal chalked off for handball inside the six-yard box and despite the loss of Hulse, the visitors were still causing Chelsea some concern.
Kazim-Richards proved he was not afraid to shoot whenever the opportunity presented itself by testing Cech for a second time in the game.
But the Czech international once again proved to be immaculate in his timing as he went down to clutch the ball at the foot of the right-hand upright.
The home side were content to keep possession for long periods and should have made it three seconds before the interval but Frank Lampard just failed to make the most of a cross by Wright-Phillips.
The game re-started with Chelsea having replaced Frank Lampard with Michael Ballack during the interval.
And it was the Germany international who came closest to adding to Chelsea's lead in the second half when he sent a 25-yard effort just wide of Paddy Kenny's right-hand post in the 53rd minute.
But Ballack had better luck four minutes later after Robben was fouled by Gillespie on the left flank.
Wright-Phillips swung over the free-kick and Ballack rose highest to glance a header into the net from six yards.
Just when United must have thought their afternoon could not get any worse, Mourinho elected to send on top scorer Didier Drogba in place of Shevchenko in the 65th minute.
The Ukrainian was given a standing ovation as he left the field for his outstanding display.
Left-back Ashley Cole was also replaced by Paulo Ferreira as Mourinho looked to rest as many of his players as possible before the FA Cup quarter-final replay.
Moments later Chelsea almost made it four when Wright-Phillips sent 20-yard low drive just wide of the target.
But Chelsea were more than content to see out the end of the contest and resorted to lengthy spells of possession but without the penetration they demonstrated so effectively for much of the game.
It was of little consequence to Mourinho who would have been pleased by the way his players conserved their energies for Monday's all-important replay with Tottenham.