Williams dropped her serve twice in the first set, including the match's opening game, before taking a 7-6 (10-8), 6-0 decision over Ekaterina Makarova.
The first set took 77 minutes but the second was over in 29 as Williams took 70 percent -- 28-of-40 -- of the points in the second set. She had a 55-52 edge in points in the first set.
The Williams-Makarova pairing was the only second-round match on Tuesday's schedule but two seeded players fell in first-round matches.
Alize Cornet advanced when, after Cornet went up 6-1, 1-1, No. 7-seeded Simona Halep retired with an Achilles tendon injury.
Halep defeated Kerber in Sunday's final of the WTA tournament in Qatar.
Also Tuesday, Kirsten Flipkens ousted Karolina Pliskova 6-1, 7-5 and Annika Beck beat Samantha Stosur 1-6, 6-1, 6-4.