Wearing a long-sleeve undershirt on yet another chilly day, Sinner only faced one break point in a one-sided clash to make it 10 straight victories at the majors this year after his Australian Open triumph.
But the lanky Italian had spent the days in the lead-up to Roland Garros nursing a hip problem that threatened to spoil his plans of winning a second major title.
"I worked on certain movements on the court. You can prevent them a little bit in the gym, but you have to go through in the matches because in the matches you have to move well," Sinner told reporters.
"We were working a lot trying to be in the position where I am right now. I'm happy at the moment knowing I have to improve the physical shape for the next round.
"But let's see what we can do tomorrow. Rest is very important in Grand Slams, so I'll try to rest as much as I can. Tennis-wise, I felt quite good on the court trying to mix up the game a little bit more like I used to do."
Kotov, who was hoping to beat a second Grand Slam champion in a row after eliminating Swiss Stan Wawrinka in the previous round, got off to a fiery start but Sinner was still a level above him in the first set.
He got another early break in the second to move two sets up and the same pattern was repeated in the third as Sinner wrapped up victory with an ace on match point.
He had also beaten Kotov in straight sets in the Madrid Masters in April but said Friday's clash was very different.
"I'm happy to be in the next round. It was a tough match. He's a very good player. I played against him not so long ago, so he changed a couple of things," said Sinner, who now faces Austrian Sebastian Ofner or local favourite Corentin Moutet.
"The general physical shape isn't where I want it to be. We try to prepare my body in the best possible way," Sinner added.
"The weather today was also different. It was very cold, so it's also different to play. The balls and the court are heavy. But these are situations you have to go through, you have to accept, and I'm trying to look forward."