The biggest upset of the day came when Elena Vesnina, fresh off her victory at Indian Wells, suffered a stunning 3-6 6-4 7-5 loss to world number 594 Ajla Tomljanovic.
Williams told the Miami Herald she struggled with the windy conditions.
“It wasn’t easy out there, the wind felt like a gale force,” she said. “I never saw her before. I didn’t know what to expect. I’m very impressed with her game and determination, and that will take her very far.” Top seed Angelique Kerber also prevailed in her evening match, beating Duan Yingying Duan 7-6(3) 6-2.
Croatian wild card Tomljanovic led 13th seed Vesnina 5-3 in the third set on Thursday when a thunderstorm halted play and returned on Friday to finish the job, sealing the victory on her third match point to move into the third round.
Vesnina, five days removed from the biggest victory of her career at the BNP Paribas Open, committed a dozen double faults in the two hour, 12 minute match.
French Open champion Garbine Muguruza, whose opening match on Thursday was also interrupted, fared better than Vesnina.
The sixth-seeded Spaniard trailed 46th-ranked American Christina McHale 6-0 3-2 when play was suspended on Thursday but staved off a match point in the tiebreak before emerging with an 0-6 7-6(6) 6-4 victory.
Romanian third seed Simona Halep was pushed to three sets by Japanese teenager Naomi Osaka before advancing 6-4 2-6 6-3, while seeds Timea Babos and Roberta Vinci were eliminated.
American Madison Keys made quick work of Viktorija Golubic 6-1 6-2.
(Reporting by Larry Fine and Jahmal Corner; Editing by Frank Pingue/Peter Rutherford)