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 team didn't lose its discipline, its energy or the control of the ball. We played a good match and deserved to win, 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
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.