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He had earlier set up Ander Herrera for the opening goal of the match and scored the second from a penalty that he had himself won, before Pablo Sarabia added a late third.
Moise Kean was also taken off at half-time but Tuchel, who lost Neymar to an adductor injury earlier this week, does not expect the pair to spend any time onthe sidelines.
"With Mbappe I think it's not ainjury, but more fatigue," he told Canal+. "The same goes for Kean.He took a lot of hits, which was painful. He wanted to continue but I said 'no'.
"Now is not the time to take too many risks. I really hope we don't have any new injured players."
Providing an update on PSG's other walking wounded at his post-match news conference ahead of Wednesday's trip to RB Leipzig, Tuchel said: "I hope that Leandro Paredes will resume training on Monday, but I'm not sure about Mauro Icardi."
PSG failed to register a single shot on target in the first half but were much improved in the second period as they made it seven league wins in a row to consolidate top spot.
The reigning champions have now won 70 per cent of their Ligue 1 away games under Tuchel –the best percentage for a PSG coach in their history –and the German was pleased with the mental resolve showed by his side.
"I am very happy," he said. "You've got to remember there are no spectators, so games lack that energy and atmosphere.
"It's difficult for my team. We played a very serious game today. I saw good energy, more qualities in the second half and a bit of luck in the game. 3-0 is a great victory.
"The team was mentally tired and there were a lot of changes. I knew it wouldn't be an easy game. With fatigue, it's like that. We found shorter distances in the second half, more connections. It was better."
PSG's win was not as routine as the scoreline may suggest, with Moses Simon missing a sitter from three yards in the first half and Kader Bamba having a penalty saved by Keylor Navas at 2-0.
Navas now has five clean sheets in six Ligue 1 appearances this term – only Bordeaux's Benoit Costil, with six from eight matches, has more –while no keeper to have played at least two games has a better save percentage than his 92.86.
"I think the team played a good game today," Navas, who captained the side, said after the match.
"We have a lot of injuries. There have been team-mates who have the opportunity to play and they have done it well.