The former world number one from Russia hadn't played in the US since March of 2015, before serving a 15-month doping suspension.
"I feel like I just want to hug everyone and say thank you," Sharapova told fans in a post-match interview. "It's my first match in the States in a really long time, and it's the closest thing to home for me."
The former world number one from Russia hadn't played in the US since March of 2015, before serving a 15-month doping suspension for the use of meldonium.
She returned to competition in April, but her comeback has been disrupted by a hip injury that forced her to withdraw from Wimbledon qualifying.
Sharapova, whose ranking has fallen to 171 in the world, received a wild card into the premier level tournament in Stanford, where she was tested Monday by the 80th-ranked Brady.
Sharapova got off to a brisk start. Although she needed to save three break points in the sixth game to take a 5-1 lead in the opening set, she broke in the next game to seize the set before Brady won the second.
"I had a bit of a letdown but that's the way it is," Sharapova said. "You finish a set and think you've got it, but she came out firing, capable of hitting winners and big serves."
Early in the third Sharapova fought off two break points to consolidate her lead, and wrapped up the match after two hours and two minutes.
"I feel like I face a lot of things: not competing for a long time, an opponent who's able to play some great tennis ... I feel like I'm playing catch-up against everyone who's had a head start," Sharapova said. "All that matters is that I keep playing."
Sharapova, who has also accepted a wildcard into the WTA tournament in Cincinnati -- another key warmup for the US Open -- booked a second-round meeting with seventh-seeded Ukrainian Lesia Tsurenko, a 6-3, 6-3 winner over Spain's Lara Arruabarrena.
Wimbledon champion Garbine Muguruza, who stunned Venus Williams in the final at the All England Club, is the top seed.
She will open with a second-round match against American Kayla Day, who defeated Japan's Misaki Doi 6-4, 6-2 on Monday.