United manager Mourinho, whose name was chanted throughout the afternoon by the 2,400 travelling supporters, also claimed Marcus Rashford had been naive in being shown a straight red card, just 10 minutes after appearing as a 60th minute substitute, following an altercation with Phil Bardsley.
By that stage, United were comfortably in front thanks to two goals from Romelu Lukaku and could even afford the luxury of a missed Paul Pogba penalty, won by Rashford following a foul by Ben Mee, and saved well by Joe Hart.
But, given the delicate political situation at Old Trafford currently, the afternoon was as notable for events off the field as on them.
Before kick-off, supporters had paid for a small plane to fly over the ground, towing a banner that read: "Ed Woodward, a specialist in failure".
The accusation - one which Mourinho famously directed at former Arsenal manager Arsene Wenger when he himself was in charge of Chelsea - referenced the executive vice chairman's supposed inability to deliver the United manager his desired transfer targets this summer.
But while Mourinho praised the United fans, who supported their players after the shock 3-0 home defeat to Tottenham on Monday, he also offered a hint of support for Woodward.
"In the match I'm not looking at the sky, unless I'm asking for the guy to give me help!" joked Mourinho.
"I didn't see the plane but Ed Woodward won this afternoon, 2-0.
"But I think we started winning this match because of Old Trafford, after Spurs. We lost at home, if the fans had reacted bad the team loses confidence, the week is not a good week, the team feels pressure.
"But we lost at home and the fans were amazing to the team. The team understood the direction was good and it was not a sad week, it was a very good week at work and we started the way you saw."
Despite the pre-match protest, and supporters clearly siding with their manager in any dispute between him and Woodward, the afternoon should have been a routine one after Lukaku scored twice in the first half.
After 26 minutes he rose powerfully between two defenders to head in an Alexis Sanchez cross before he reacted sharply following a deflected Jesse Lingard shot and swept the ball in from six yards.
Mourinho claimed that Pogba will remain United's penalty taker, despite his miss, should he wish to remain on duty.
But what had been an unqualified United success at Turf Moor to that point suffered slightly when Rashford, who had been cynically fouled by Bardsley, head-butted his assailant.
"I didn't see it, the only thing I can say is that is probably the experience of Bardsley, 20 years in football, against the impulse and naivety of a guy who has been in top football for three years but is still a young head," said Mourinho.
"Harsh? I don't know. You could give yellows for both and keep going, maybe."
The closing stages should have seen Lukaku claim a hat-trick, as he twice missed one-on-ones when clean through on Hart, but not even those errors could reduce Mourinho's appreciation for his efforts.
"He played very well for us, scored two important goals," said Mourinho.
"He could have scored more but maybe he was a bit tired, playing with 10 men.
"He should be leaving here with a hat-trick, easily. But the important thing is he is back to goals and we're back to victories."