World number two Federer launched his bid for a record fifth title at the Indian Wells Tennis Garden with a clinical 6-4 6-2 victory over Argentina's Diego Schwartzman which lasted a little over an hour.
Seventh-seeded Wawrinka, however, was knocked out of the ATP Masters 1000 event, losing 6-3 3-6 6-3 to Dutchman Robin Haase.
Spanish left-hander Rafa Nadal, a three-times champion at Indian Wells, also advanced in comfortable fashion as he demolished Dutchman Igor Sijsling 6-4 6-2 in an evening match lasting just 72 minutes.
Federer treated the stadium court crowd to his familiar array of blistering forehands, clean-hit backhands, power serving and delicate drop shots as he broke Schwartzman once in the opening set and twice in the second.
"I think I did very well," Federer said courtside after ending the match with a crunching forehand winner down the line. "It was a bit breezy and you had to be careful at times but it's good to get a first win.
"It was important to get off to a good start. I just tried to stay focussed and stay aggressive on returns, although that's not always easy."
Federer, who is competing at Indian Wells for a 15th time, will next face Italy's Andreas Seppi, who stunned him with a four-set defeat in the third round of the Australian Open in January.
"I'm happy to play him again," Federer said of the 30th-ranked Seppi, who booked his place in the third round at Indian Wells with a 6-4 6-4 victory over Romanian Victor Hanescu.
"I was very disappointed with the performance I had in Australia. I hope this time around it's going to go better for me. I will be prepared, there is no doubt about that."
Wawrinka, who clinched his first grand slam singles title at last year's Australian Open, was broken twice by Haase in the opening set and also in the third to be ousted after one hour and 48 minutes.
Haase, who had been beaten by the Swiss in all six of their previous meetings, will next play Czech Lukas Rosol, who battled past Slovakian Martin Klizan 4-6 6-0 6-3.
In other matches, 11th-seeded Bulgarian Grigor Dimitrov scraped past rising Australian Nick Kyrgios 7-6 (2) 3-6 7-6, taking the climactic third-set tiebreaker 7-4, and sixth seed Milos Raonic of Canada eased past Italian Simone Bolelli 6-3 6-4.
(Editing by Peter Rutherford/Patrick Johnston)
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