For their manager, Antonio Conte, this was a troubling display. He lost goalkeeper Thibaut Courtois to injury and then Marcos Alonso to illness in the warm-up, but that did not explain how flat and overwhelmed his team were.
Mourinho had complained about tiredness but it was Chelsea who looked jaded, who looked, in fact, like a favourite and front-runner desperately straining for the finish line. There are 18 points to be won. They need to win five of those games to be mathematically certain, if Spurs keep winning, but suddenly it is no longer a procession. As recently as March 18 Chelsea were 13 points clear.
Suddenly there is that seed of doubt. Suddenly, also, pressure on Spurs, who have played superbly to stay in touch - and, fascinatingly, the sides meet this weekend in the FA Cup semifinal.
There was also pressure on United and Mourinho. He needed this performance, the best he has produced so far as United manager, not just to stay in touch with the top four but also to show he has the ability to out-tactic a vibrant coach like Conte. The fire still burns for Mourinho.
"A special performance because it was a special opponent," Mourinho later said. "The leader. We played well. We gave them problems ... so these three points are phenomenal." They were, to be fair.
Mourinho rested Zlatan Ibrahimovic, and there was a brilliant response from Marcus Rashford, who, along with Jesse Lingard, had the pace and movement to trouble Chelsea.
There was a clear handball in the build-up to the first goal in the seventh minute - United's quickest this season - despite Herrera's weak argument afterwards that it was not deliberate, as he intercepted Nemanja Matic's pass with an outstretched arm. After that his pass was incisive as he slid the ball past David Luiz with Rashford running on and cutting his shot back across Asmir Begovic and into the net.
Old Trafford erupted. Eric Bailly and, in particular, Marcos Rojo, took the fight to Diego Costa. Herrera remained shackled to Hazard and Chelsea were knocked out of their stride.
Not once did United relent. Mourinho coaxed, cajoled and ordered. He demanded more and more energy and effort, while Conte looked curiously inactive, a bit like his team, wearing and then disposing of a baseball cap to accompany his suit. His attire jarred, just as his players did on the pitch.
Nothing was happening for them. Chelsea were unsettled at the back, and that was summed up by United's second goal, which gave them an iron grip. Herrera's shot ricocheted off N'Golo Kante and spun beyond keeper Begovic.
Chelsea had no reply. United are now 22 matches unbeaten - the longest run in Europe's top five leagues - with Mourinho adding: "Normally you win the title if you are 22 matches unbeaten, and we are struggling to finish in the top four." But this was a performance of champions.
• Liverpool climbed above Manchester City into third with a 1-0 away win over West Bromwich Albion.
Roberto Firmano got the goal, heaving home from a James Milner freekick.
