"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 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."
"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.
She will open with a second-round match against American Kayla Day, who defeated Japan's Misaki Doi 6-4, 6-2 on Monday.
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