Federer, seeking his second Grand Slam title of the year and his sixth championship at this event, defeated Bjorn Phau 6-2, 6-3, 6-2. Next up for Federer will be No. 25 seed Fernando Verdasco, who outlasted Albert Ramos 7-6 (7-4), 5-7, 7-6 (7-3), 6-4.
The Wimbledon title Federer won in July was the 17th Grand Slam championship of his career. It ended a drought of nine straight major championships without a crown. Federer then lost in the gold medal match at the Olympics to the player he defeated in the Wimbledon final -- Andy Murray.
Tsonga was ousted by Martin Klizan 6-4, 1-6, 6-1, 6-3 in just over 2 hours. Tsonga reached the quarterfinals of this tournament a year ago.
Mardy Fish advanced past the second round with a huge comeback. Seeded 23rd, Fish defeated Nikolay Davydenko 4-6, 6-7 (4-7), 6-2, 6-1, 6-2.
No. 16 seed Gilles Simon earned a third-round matchup with Fish thanks to a 6-4, 4-6, 6-4, 6-4 decision over Jimmy Wang.
Other winners in the second round included Nicolas Almagro, Sam Querrey, Jack Sock, Tomas Berdych, Milos Raonic, Marin Cilic, Kei Nishikori and Jeremy Chardy.
The victories by Fish, Sock and Querrey put three Americans through to the third round in the same quarter of the draw that includes Federer.
Wins by Federer and Fish in the third round would create a matchup between those two players early next week.