Marcus Rashford confidently converted from the spot to send Ole Gunnar Solskjaer's side into the quarter-finals of the Champions League.
Paris Saint-Germain were leading the game 3-2 on aggregate when Diogo Dalot fired a shot at goal from distance.
The strike hit Kimpembe's arm and flew out of play for a corner kick.
His back was turned, but the referee decided to check the footage with the video assistant referees.
Damir Skomina charged back onto the pitch and pointed to the spot to give United one final chance in the last-16 tie.
Rashford sent PSG crashing out of the competition when he stuck his first ever competitive penalty for United past Gianluigi Buffon.
After the match, Old Trafford Rio Ferdinand said: "I don't think it's a penalty, but turning your back, as a defender, you get punished for things like that."
Fellow pundit Michael Owen added: "I don't think it's a penalty in a million years. It's not a penalty for me or anybody in this room."
But the former Liverpool forward praised Rashford's confidence when he stepped up to the spot.
After he scored the winner, Rashford revealed how difficult it was to wait on the pitch while the referee made his decision.
The 21-year-old said: "It's probably the hardest thing the wait before, but it's all part of the game.
"And those moments are what we live for you want to get through those moments and be smiling after."
Romelu Lukaku, who scored United's first two goals, showed his class by consoling Kimpembe after the final whistle in France.
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