The wind, cold and drizzle made for difficult conditions in Paris and Federer was surprised by how well Schwartzman handled it all. But Federer still managed to advance in straight sets, 6-3, 6-4, 6-4.
The 21-year-old from Argentinean qualifier was making his Grand Slam debut and his victory over fellow qualifier Gastao Elias in the first round was only the second Tour-level win of his career.
It was Schwartzman who drew first blood, breaking Federer’s serve in the third game but the Swiss 2009 champion struck back immediately to draw level and win four games in a row en route to taking the set.
A tight second set was decided in game 9 when Federer broke for a 5-4 lead and the Swiss broke early in the third to secure the win.
“I think it was kind of tough all the way through, for me,” said Federer.
“I didn't feel relaxed for the entire match. I've always felt he had a little bit of an upper hand from the baseline.
“I feel he was doing a really good job being aggressive and making good plays. I think he handled the conditions really well.”
The 17-time major champion next faces Russian veteran Dmitry Tursunov, who stretched him to two tiebreak sets in their previous meeting.
“Tursunov is a different player altogether versus Schwartzman today,” said Federer.
“He tried more with his serve, but also with the forehand. And also I played against him at Indian Wells. It was 7 6, 7 6, that's how I defeated him. It was a tough match. But at least I know Dmitry, I didn't know Schwartzman at all. I didn't know if he was a great player, average, or not really good.”
Earlier in the day, No2 seed Novak Djokovic was happy he handled the constantly-changing conditions well as he easily dismissed Frenchman Jeremy Chardy 6-1, 6-4, 6-2 in 92 minutes.
He says he’s aware of all the upsets happening during the first two rounds and says it’s important not to underestimate any opponent.
“In the Grand Slam we all know that in the opening rounds that the lower ranked players have a lot of motivation to play their best and to win against top players on the big stadiums,” said the second seeded Serb.
“I just saw that Serena (Williams) also lost. So it's definitely a surprise to see the big favourites coming out. But again, you can never underestimate any opponent in a Grand Slam.”
He faces Croatian Marin Cilic next.
Jo-Wilfried Tsonga gave a clinical performance against Austrian lefty Jurgen Melzer advancing 6-2, 6-3, 6-4. “It was a very good match, clearly. I know I can do even better,” said Tsonga, who plays No22 seed Jerzy Janowicz next.