Federer, who took more than a month off after losing the Wimbledon final to Novak Djokovic, beat Roberto Bautista Agut 6-4, 6-4, improving to 4-0 over the Spaniard without the loss of a set.
But the 34-year-old said that he needed time to adjust again to match conditions after his hiatus.
“It was a good win for me, it can only get tougher from here,” said Federer, seeking a record seventh title here.
“I haven't played in a long time and I felt a bit rusty at times in the first set,” he said.
“I need matches right now, so it was good to start well here,” the Basel native said.
“I'm happy I got through this first one — now I know what it's about.
“I have a day off tomorrow where I can think about how things went today, where I need to improve.”
US Open winner Marin Cilic, the seventh seed, beat Joao Sousa 6-4, 6-2, while Spain's Feliciano Lopez stopped Canadian Milos Raonic 7-6 (7/4), 6-4 as the ninth seed lost an opening match for the second straight week.
Sam Querrey put out John Isner 6-3, 7-6 (7/3) and South African 15th seed Kevin Anderson defeated Leonardo Mayer 7-6 (7/5), 3-6, 6-1.
Controversial Nick Kyrgios was dumped out, a 6-2, 6-1 first-round victim of French 12th seed Richard Gasquet.
Kyrgios, building a reputation as the bad boy of the game, was unremarkable in the match, which lasted for only 56 minutes.