The fourth-seeded Swiss, gunning for a record-extending 18th grand slam title, wasted 17 break points before setting up a meeting with Latvia's Ernests Gulbis but did not seem too bothered.
"After three rounds, I have got all the information," Federer told a news conference.
"Today it was a tough match, I had to defend well because he was a very aggressive player. Against a previous player it was a matter of getting in the groove.
"The first round was quite okay, but I've got my bearings now, my landmarks on court. I know what are my assets, what are my weaknesses. Serve, return, that's quite okay."
Federer was indeed barely troubled on his serve by 31st seed Tursunov, who lost the first set when Federer broke decisively in the 12th game.
The 2009 Roland Garros champion threw away four set points in the second before Tursunov took the tiebreak 9-7.
The third set was far easier for the crowd favourite in Paris but he continued to waste opportunities to break Tursunov's serve, including seven in the fifth game of the final set.
But the Swiss broke for 4-3 and won the three-hour match on his first match point with a forehand winner.
Tursunov had treatment on his leg during the third set.
"It's a groin (injury), so basically I can't lift my leg to push to the sides, to run side to side, so it was pretty difficult. Anything on the return, can't really move to the side," Tursunov said.
"Then when he was trying to drive me around the court with dropshots, that's basically what bothered me the most."
Next up for Federer is an opponent who beat him on clay at the Rome Masters in 2010.
"He has a great serve and he's very enterprising on the second serve. His backhand is very simple. It works well with a lot of power," Federer said of the 18th seed.
"He's able to hit the backhand above his shoulders, so he's a very good player. Year after year he moves better on court. I think that he is more determined. He has a great game, and he can do lots of great things, thanks to his game."
Nothing that can scare Federer, though.
"Of course I'm quite ready to play against Gulbis," he said.
Results from the French Open Men's Singles Round
13-Jo-Wilfried Tsonga (France) beat 22-Jerzy Janowicz (Poland) 6-4 6-4 6-3
10-John Isner (U.S.) beat 17-Tommy Robredo (Spain) 7-6(13) 7-6(3) 6-7(5) 7-5
6-Tomas Berdych (Czech Republic) beat 27-Roberto Bautista (Spain) 6-1 6-2 6-7(4) 6-4
2-Novak Djokovic (Serbia) beat 25-Marin Cilic (Croatia) 6-3 6-2 6-7(2) 6-4
4-Roger Federer (Switzerland) beat 31-Dmitry Tursunov (Russia) 7-5 6-7(7) 6-2 6-4
18-Ernests Gulbis (Latvia) beat Radek Stepanek (Czech Republic) 6-3 6-2 7-5
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- Ernests Gulbis