United manager Jose Mourinho started with top scorer Zlatan Ibrahimovic on the bench but delivered a tactical masterclass against his former club, largely nullifying the threat from the usually risky Eden Hazard.
Mourinho said: "He's exhausted - very tired".
For United, meanwhile, manager Jose Mourinho chose to leave Ibrahimovic on the bench with the 35-year-old top scorer having faced Anderlecht in Thursday's Europa League quarter-final first leg.
(Adam Davy/PA via AP). We fight until the end.
It was a goal rooted in controversy from Chelsea's point of view as United midfielder Herrera appeared to handle to win back possession.
"This is a game between two teams that are in contention to win the league this season".
"Maybe we didn't "rest" players ahead of Thursday (when United play Anderlecht in the Europa League), we just chose the team we thought was the best team", Mourinho told Sky Sports at Old Trafford.
The decisions paid off brilliantly, with Rashford and Herrera scoring the goals and being the star performers at Old Trafford.
Chelsea will host Southampton in their next Premier League game at Stamford Bridge on Tuesday 25 April. Hazard barely had a meaningful touch.
"I think they are a good team".
Chelsea might be starting to wobble. "I wasn't feeling good in the sense of I was feeling exhausted but it is not an excuse because I still had to do much more and much better than I did".
Still, the pressure is certainly on the leaders now.
He said: "The pressure is normal". The league is open.
Mourinho said: "Normally you win the title if you are 22 matches unbeaten and we are struggling to finish top four". "We've played many games and I've played in nearly all of them".
Chelsea's second loss in four games has reopened the title race, offering hope to second-placed Tottenham who are just four points behind with six games to go. Moment of the match The stage was set for a pulsating game in the seventh minute as Herrera slid Rashford in on goal with a fine defence-splitting pass.
Stand-in captain Ashley Young was unable to get away a shot but the ball fell for Herrera to produce a thumping strike, taking a deflection on its way past Begovic. On a rare occasion he left Hazard's side, Herrera popped up in Chelsea's area in the 49th minute to smash a deflected shot high into the net from 18 meters.
Chelsea, meanwhile, are without goalkeeper Thibaut Courtois but Victor Moses returns.
Manchester United face Chelsea on Sunday with a burden of an eight match winless streak against the Blues.
United have not lost in the league since October, but remain outside the top four. It meant main centre-back David Luiz had to cover for the rusty Zouma while also dealing with Rashford.