The Serb did not get a break chance in the opening set, but dominated the tiebreaker and took a quick 3-0 lead in the second. He said he would be working on a few things before his third-round match against Colombian Alejandro Gonzalez, a 6-4, 2-6, 7-6 (7/5) winner over Croatian Ivan Dodig.
Also on Sunday, Roberto Bautista Agut of Spain bounced fourth-seeded Tomas Berdych 4-6, 6-2, 6-4.
Bautista, ranked 53rd in the world, used a punishing ground game to notch his third career win over a top-10 player.
“I played unbelievable,” Bautista said. “I was not serving very well, I had to play my best tennis from the baseline to win the match.”
The 28-year-old Czech, an Australian Open semi-finalist who won in Rotterdam this year, arrived in California after a runner-up finish to Federer in Dubai and was at a loss to explain his off-key outing.
“Anything I touched today was basically bad and was wrong,” Berdych said. “Definitely my worst match that I had this year.”
Men’s sixth seed Juan Martin del Potro had been slated to open his campaign, but the Argentine withdrew with a left-wrist injury.
In the women’s singles action, second-seeded Agnieszka Radwanska of Poland led the way into the fourth round.
Radwanska, ranked third in the world, thumped 48th-ranked German Annika Beck 6-0, 6-0.
Beck did what she could to make a stand — notably in the fourth game of the second set, which went to deuce seven times — but was unable to get on the scoreboard in a match that lasted just 67 minutes.
Radwanska next faces France’s Alize Cornet, who battled for 3 hours, 26 minutes to beat the 14th-seeded Spaniard Carla Suarez Navarro 6-7 (4/7), 7-5, 6-3.
It was the second-longest match on the WTA Tour this year, after Maria Sharapova’s 3 hour, 28 minute win over Karin Knapp at the Australian Open.
Cornet fought off triple match points, serving 4-5, 0-40 in the second set en route to the victory.
“I don’t know how I won this match,” the Frenchwoman said, adding that fatigue may have worked in her favor in the third set. “The good thing when you are tired is you don’t ask too many questions, you just hit the ball. That’s better for me.”