The Mexican goal-poacher, looking suspiciously offside, tucked in the winner in the 75th minute to kill off a vibrant Chelsea side who had battled back from 2-0 down before having Branislav Ivanovic and Fernando Torres sent off by referee Mark Clattenburg in the final half-hour.
Torres's dismissal, for diving, led to a furious touchline row between Chelsea manager Roberto Di Matteo and his United counterpart Sir Alex Ferguson who later said the Spaniard had deserved to go despite replays suggesting he was fouled.
Clattenburg was later the subject of a complaint by Chelsea over "inappropriate language" towards two players.
A David Luiz own goal gave United the lead after four minutes and Robin van Persie fired the visitors 2-0 ahead soon after with his seventh league goal of the season.
Chelsea roared back with Juan Mata's free-kick and a Ramires header either side of the interval and United were on the ropes until Serbian right back Ivanovic was sent off just past the hour mark for bringing down Ashley Young.
Worse followed for Chelsea five minutes later when Torres tumbled on the edge of the area after apparent contact by Jonny Evans and was shown a second yellow card.
With the home crowd howling its disapproval and tempers fraying on the touchline, Hernandez - on as a substitute for Tom Cleverley - tapped in Rafael's fierce cross while standing almost on the goal-line.
United's first win at Chelsea for 10 years lifted them back above neighbours Manchester City into second place on goal difference with 21 points, one point behind Chelsea who had ample reason to feel hard done by.
"We must be disappointed that key decisions were wrong," Di Matteo told reporters.
"At 2-2 we looked like the team that was going to win the game. It was a good game between good teams and the official ruined it. Key decisions have to be right and you don't want the referees to have such a big influence."
Torres, not surprisingly, got little sympathy from Ferguson although the Scot acknowledged his side had enjoyed some luck.
"The decision the referee has to make is whether the striker has chosen to go down," he told Sky Sports. "He was through on goal - I don't know why he has gone down.
"I think it's his own fault. We've never got breaks down here and had some terrible decisions against us in the last few years. But today we have got a little break for the goal - Chicharito may have been offside."
Earlier the Merseyside derby also proved a typically feisty affair as Everton recovered from 2-0 down to draw 2-2 with Liverpool at Goodison Park.
WRONGLY RULED OUT
Liverpool striker Luis Suarez was in the thick of the action as his shot was turned into his own net by Leighton Baines after 14 minutes.
The Uruguayan celebrated with a theatrical dive in front of Everton boss David Moyes, who had been critical of Suarez's habit of going to ground in the build-up to the game.
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