Federer, seeded second, had little trouble in a 6-3, 6-1 victory over No. 8-seeded Janko Tipsarevic and Ferrer, the No. 4 seed, topped sixth-seeded Juan Martin del Potro 6-3, 3-6, 6-4 in the second Group B game.
With world No. 1 Novak Djokovic and third-seed Andy Murray picking up wins in Monday's Group A play, the top four seeds have begun the eight-player invitational tournament with victories. The top two players in each group move into the semifinals Saturday.
Federer, the two-time defending champion at the event, didn't see a break point against Tipsarevic.
Federer moved out to a 3-0 lead in the opening set and won the last six games in finishing off a 69-minute match. His 51 percent first-serve figure wasn't impressive but Federer only dropped eight points over eight games serving. That allowed him to improve to 6-0 in his career against Tipsarevic.
Ferrer had the only break of the first set to take the lead. But del Potro fought off four break points for a hold at and then posted a break for a 3-1 lead and he went on to even the match.
Ferrer had a 3-0 lead in the second set but del Potro worked back to 4-4. Ferrer answered with a hold at love and then broke del Potro -- also at love -- for the third time on the day to end the match.
Djokovic takes on Murray in the first Group A match Wednesday. Both won matches Monday so the winner Wednesday likely advances to the tournament semifinals.
Also in Group A Wednesday, Tomas Berdych goes against Jo-Wilfried Tsonga with the loser likely eliminated from advancing.