The third and fourth Chelsea goals were down to mistakes by young defender Scott Wootton, who gave away the penalty which Eden Hazard scored right at the end of normal time and then inadvertently played in Daniel Sturridge with a weak back header for another.
Ramires made it 5-3 before a Ryan Giggs penalty pulled United back to within one in another topsy-turvy match following Arsenal’s remarkable 7-5 win at Reading on Tuesday night.
Sunday’s Barclays Premier League game between the two teams was overshadowed by the accusations of "inappropriate language" against referee Mark Clattenburg, but this time the football took center stage.
United took the lead in the 22nd minute following a defensive mix-up by Chelsea, Giggs taking advantage by scoring with a well-placed shot into the bottom corner from the edge of the area.
David Luiz brought Chelsea level nine minutes level with a coolly-taken penalty after Alexander Buttner had chopped down Victor Moses.
But Javier Hernandez, who got the winner on Sunday, continued his fine record against the Blues with another smart finish two minutes before the break. Again the hosts came back, this time Gary Cahill powering home a Juan Mata corner in the 52nd minute.
But they simply could not keep things watertight at the back and were cut apart by a superb combination between Anderson and Nani seven minutes later, the Portuguese dinking a beautiful finish past Petr Cech.
Chelsea were denied a strong penalty claim when the ball appeared to strike Wootton’s arm, adding to their list grievances following the two red cards in the league game.
But they did get a penalty in the fourth minute of injury time as this time Wootton was punished for a push on Ramires and Hazard rolled his penalty low down the middle.
Worse was to come for Wootton seven minutes into extra time as his attempted header back was too short and Sturridge rounded Anders Lindegaard to score.
Ramires added another in the 116th minute, dancing around the Dane for number five.
The visitors were not done, Giggs slotting home from the spot after a foul on Hernandez, but there was not enough time to get an equalizer.