Sunday's slump for PSG at the Parc des Princes sent the first place to Lille, who defeated Bordeaux 2-1 earlier in the day. Lyon is second on goal difference while PSG is one point off in third.
Mbappe scored from the penalty spot in the 42nd minute against Istanbul Basaksehir on Wednesday, giving his side a three-goal lead at half-time after Neymar had already scored a brace.
The match, which started on Tuesday, had been halted after 14 minutes when both sides walked off amid alleged racist abuse from fourth official Sebastian Coltescu to Basaksehir coach Pierre Webo, reports Xinhua news agency.
The midfielder was sent off in the 70th minute for a second yellow card after his challenge on former United midfielder Ander Herrera just after United had gone 2-1 down when Marquinhos scored.
"I felt like it was tough, but that was of our own making. We simply stopped playing in the second half, we didn't stick to our plan and we didn't work hard enough," the club's official website quoted Tuchel as saying.
We defended like crazy, and it's true we lost a lot of ball, but I also know what condition we're in physically. A lot of the players lack rhythm, conditioning, the players are physically and mentally tired and a lot of them aren't used to playing these types of games with us
PSG secured a 1-0 win over RB Leipzig in the Champions League here on Wednesday. After the win, Neymar took to Instagram and wrote in Portuguese: "Today the important thing was the 3 points, no matter how.
"We worked very hard on pressing high up the pitch early in the match. We did it very well and winning back possession enabled us to score the first two goals. That was a real positive for us tonight," the club's official website quoted Tuchel as saying.
All the goals came in the second half, with Ander Herrera opening the scoring two minutes after the restart and Mbappe converting a 65th-minute spot-kick before Pablo Sarabia secured the points late on
The home side were put under pressure by Julian Nagelsmann's team but substitute Rashford struck three times after coming on in the 63rd minute to put the result beyond doubt.
Rashford, who scored the winning spot-kick when United knocked PSG out in 2019, drilled home a low shot three minutes from the end which won a thrilling Group H contest at a near-empty Parc des Princes.
Mbappe netted late to give France a 2-1 win at Croatia two days ago in the Nations League.
Nimes center half Loick Landre was sent off after 12 minutes for a chest-high high tackle on midfielder Rafinha.
