Both 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 last night [Tuesday].
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 centre stage.
United took the lead in the 22nd minute following a defensive mix-up by Chelsea, Ryan 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 sendings off 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, who up till then had been awful, 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 equaliser.
Elsewhere, Norwich scored twice in the final seven minutes to come from behind and 2-1 at home to Tottenham, who also missed a late penalty.
A strong Spurs side went in front through Gareth Bale in the 66th minute, but a Jan Vertonghen own goal in the 84th minute levelled the scores.
And the Canaries, struggling in the league, completed the turnaround three minutes later as Simeon Jackson followed up to tap home after fellow substitute Grant Holt's header was parried.
Clint Dempsey had the chance to make it 2-2 from the spot a minute later, but his low effort was kept out by Mark Bunn in the Norwich goal.
Brendan Rodgers saw his Liverpool side, the holders, crash to a 3-1 defeat at home to former club Swansea.
Rodgers paid the price for fielding a weakened team as Chico headed the Swans in front just after the half-hour mark.
A Nathan Dyer finished made it two 18 minutes from time and, even though Luis Suarez, off the bench, pulled one back four minutes later by heading home a Steven Gerrard free-kick, Jonathan de Guzman killed the Reds off in stoppage time.
Wednesday's Capital One Cup Results