Federer took a while to get going, letting an early lead slip in the first set, but he was rarely threatened by 6ft 6in Querrey and took the match in one hour 35 minutes.
"He's an up-and-coming player who has got a good serve and big shots. On the day you don't know what's going to happen and that's why it's sort of nerve-wracking.
"Practice is one thing but today the atmosphere is different, the court full, the pressure is there. That's why I'm sort of relieved getting through the first one.
"From now it should get a little bit easier."
Elsewhere, Tommy Robredo, the 12th seed, rallied to beat former finalist Guillermo Coria 5-7 6-4 6-1 6-4.
Coria was playing his first Grand Slam match for nearly two years after back and shoulder injuries.
"I thought about retirement," said the former world number three. "A month ago I didn't think I would play here but Roland Garros means a lot to me. It's like another home.
"In the last three weeks the situation has changed and I'm eager to be back on tour."
Eleventh seed Tomas Berdych of the Czech Republic made an almost perfect start as he thrashed Australian Robert Smeets 6-1 6-0 6-0.
Chile's Fernando Gonzalez, the number 24 seed, was another comfortable winner, crushing Uraguay's Pablo Cuevas 6-3 6-3 6-1.
But Guillermo Canas - three-times a quarter-finalist at Roland Garros - suffered a surprise 7-6 (8-6) 7-6 (7-3) 7-6 (8-6) defeat by American wildcard Wayne Odesnik.
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