The Mexican goal-poacher, looking suspiciously offside, tucked in the winner in the 75th minute to kill off a vibrant home 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 an hour of the Premier League clash.
Clattenburg was later the subject of a complaint by Chelsea over "inappropriate language" towards two players.
Torres's dismissal – for diving – led to a furious touchline row between Chelsea manager Roberto Di Matteo and his United counterpart Alex Ferguson who later said the Spaniard had deserved to go despite replays suggesting he was fouled.
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 goalline.
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.
Suarez headed Liverpool's second after 20 minutes but Everton recovered before halftime with goals by Leon Osman and Steven Naismith earning them a deserved draw.
But Liverpool's South American had a very late effort wrongly ruled out for offside.
Moyes had no sympathy for Suarez and was angry that he trod on the leg of Everton defender Sylvain Distin in the second half. He liked the joke dive, though.
"I thought it was great, I would probably have done the same, but he is going to have to dive in front of a lot of managers now," Moyes said. "He was a very lucky man to stay on the park because of his tackle."
Everton fell out of the top four after Tottenham Hotspur beat struggling Southampton 2-1 away with Gareth Bale on the scoresheet against his old club. Newcastle United beat West Bromwich Albion 2-1.
Chelsea and United drew 3-3 at Stamford Bridge last season in the Premier League and the latest chapter in their rivalry proved to be another classic encounter.
United, who meet Chelsea again this week in the League Cup, made a blistering start as they went 2-0 ahead after 12 minutes.
Chelsea were guilty of giving away possession and when Wayne Rooney cut a pass back for Van Persie, the Dutchman's shot cannoned off the bar and ricocheted off Luiz into the net.
The early blow disrupted Chelsea's composure and they fell further behind to a devastating United counter-attack.
Antonio Valencia made ground down the right and his cross was perfect for Van Persie to fire past Petr Cech with Chelsea's defence all at sea.
Chelsea, again playing with Oscar, Eden Hazard and Juan Mata in an attacking formation behind Torres, cleared their heads and a minute before halftime Mata curled an unstoppable free kick past David de Gea to give them hope.
They were level after 53 minutes when Ramires climbed to head in Oscar's dinked cross in a crowded area.
The game seemed to have swung Chelsea's way but Ivanovic was dismissed for an inadvertent trip on Young and a few minutes later Torres tumbled as he raced through but, to his horror, got up to see a red card being waved at him.
Hernandez then rubbed salt into Chelsea's wounds, leaving the home crowd chanting "3-2 to the referee". – Reuters