Settling into his rhythm, Federer broke again to lead 4-3 and converted his first set point with a forehand winner.
Mannarino, who lost to Federer in the third round of the U.S. Open, sent a two-handed backhand long to concede a 3-2 lead in the second set. Federer broke serve again by hitting another forehand winner and clinched the match with a serve that Mannarino could not return.
Earlier Monday, Lukasz Kubot of Poland beat Daniel Gimeno-Traver of Spain 7-5 (6), 6-2, and Tobias Kamke of Germany beat Victor Hanescu of Romania 6-4, 6-4.
Alexandr Dolgopolov of Ukraine was playing Kenny de Schepper of France in the late match.