Goals at the start of either half from Marcus Rashford and Ander Herrera condemned Mourinho's former side to their second defeat in four games at Old Trafford.
The Blues' lead over second-placed Tottenham is now down to four points with six games remaining, while United boosted their own hopes of reaching the top four by extending their unbeaten league run to 22 games.
The Red Devils are four points behind fourth-placed Manchester City, with a trip to the Etihad Stadium on the horizon on April 27.
Former United captain Neville was impressed by Mourinho's team as they shone despite Zlatan Ibrahimovic and Henrikh Mkhitaryan starting on the bench.
He told Sky Sports: "It was the best experience for the [United] crowd.
"I underplayed it a little bit in the pre-match interview... I'd just walked from the gantry through quite a few people that I know who said 'look at that team he's picked!' thinking whether it was going to be a positive day.
"That was a brilliant performance, they were all nine out of 10. Every single one of them played absolutely fantastically.
"Chelsea didn't turn up. Where was Conte today? The manager?
"You can talk about the players, but the manager's been so active on the touchline all season and you're expecting him to get them going, him to raging up and down that touchline."
"He seemed subdued today and looked like he lacked belief.
Regarding referee Robert Madley's decision not to award a handball against Herrera in the build-up to Rashford's goal, Neville said: "For me Chelsea didn't turn up but United were fantastic - yeah [there was] a little bit of luck I think on the goal with the handball, I think any team would want that for them.
"It's not a deliberate handball but I think if you're a United player and it goes the other way you would want it for you."