Scott McTominay opened the scoring in the first half when Diogo Dalot found the net with a clever cross which the Scots were first on.
Just before the break, Harry Maguire’s header doubled the lead, and after an hour Manchester United looked set to seal their place in the final when Bruno Fernandes tripped around the penalty area before making it 3-0 with a free-kick.
But Coventry would match it.
In the 73rd minute, United completely lost themselves in defense and left Ellis Simms completely clean with the ball in front of the goal and 1-3 was a fact.
Six minutes later, Callum O’Hare made it 2-3 after his shot was headed in by Aaron Wan-Bissaka, who was unfortunate as he tried to cover.
And in stoppage time, the reduction came after Wan-Bissaka was unlucky again and answered for a hand.
Haji Wright was the safety himself from eleven meters and forced extra time with his 3-3 goal.
Extra time ended goalless after Coventry had a goal ruled out for offside by a narrow margin in the final minute.
The match was decided on penalties, with United drawing the longest after the home side’s Ben Scheaf sent his penalty high over the bar.
Now they can look forward with bated breath to the final where they will face city rivals Manchester City.
– We found a way to win, says Harry Maguire to ITV.
– This sums up our season, we had good control and played well for 60 minutes and then we start conceding goals from nothing.
– Then I don’t know what happened, it felt like the whole world wanted Coventry to win. We showed good character and it was important to win the shootout.
Coventrys manager: Mark Robins:
– To come back from 0-3 is incredible. We played high quality football. We are very disappointed. We had one in the crossbar and a goal disallowed. It was a difficult match. But I couldn’t be prouder of the guys. They did amazingly well. I think they have done all of Coventry proud.
The FA Cup Final will be played on May 25 at Wembley.