The reigning Australian Open champion beat the qualifier 6-4, 6-1 in one hour and 28 minutes in her opening game of the tournament, having received a bye for the first round, reports Efe.
Wozniacki has struggled with injuries since her winning the title at Eastbourne in June, suffering first-round exits at Montreal, Cincinnati, and Tokyo.
Against Peterson, the Dane was always in control, making just four unforced errors and first-serving well over 70 percent throughout the match.
After an early break gave Wozniacki a 3-1 lead, she broke the Swede again to set her up to serve for the set at 5-2.
She will face Puerto Rico's Monica Puig in the round-of-16 on Wednesday.