Goals at the start of either half from Rashford and Ander Herrera condemned Mourinho’s former side to their second defeat in four games.
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.
Mourinho, though, praised the performance of 19-year-old forward Rashford and his teammates for a dominant Old Trafford showing.
“He played fantastically well, I think he did also a very good game at Stamford Bridge in the FA Cup,” Mourinho said.
“Today he scored and it was at the beginning of the match which gave the team confidence and stability. The kid played fantastically well, but everybody fought and did what they had to do.”
Mourinho set his team up in a similar way when United fell to a 1-0 defeat at Stamford Bridge in the FA Cup last month after being reduced to 10 men following Herrera’s red card.
“That game was totally controlled when we played with 11 players, and only the decision that made us play with 10 players gave Chelsea a chance to be dominant,” he said.
“We knew that playing this way would be very difficult for them.”
United have a Europa League quarter-final tie with Anderlecht on Thursday, but Mourinho said that he will continue to push forward on both fronts:
“I cannot yet give up the Premier League. We have to try and if one day we are in the Europa League and in the Premier League the distance is too big, then we have to prioritise and nobody can criticise us if in the last matches of the league we do it in a different way.
“But while it is mathematically possible, we have to go with everything we have.”