Sharapova was due to play Spain's Carla Suarez Navarro in her first-round match, but the late withdrawal of fifth-seeded Anastasija Sevastova of Latvia led to a reshuffle of the draw.
Suarez Navarro became the tournament's eighth seed and Sharapova played her first match of 2011 against Brianti, who entered the main draw as a lucky loser after being beaten in the last round of qualifying.
Sharapova took 90 minutes to down Brianti and said she was unfazed by the late change.
"We spend so much time training and out-of-tournament competition, it's great to be in the atmosphere of a crowd," she said. "The change of opponent was different, because I warmed up pretty early. I headed back and took another rest and came back. That was the only hiccup today."
Sharapova is looking to rebuild her game and claw back in the world rankings this season after spending most of the past two years battling shoulder injuries.
She looked fit and sharp Monday, playing with typical athleticism -- and at her usual volume -- but she lacked some of the accuracy that comes from match play.
The Russian also found Brianti, who had played her final qualifying match on Monday, a grittier opponent than she might have expected in a lucky loser.
Sharapova saved a break point in her opening service game before breaking Brianti to love in the fourth game for a 3-1 lead. She broke again to lead 5-1, then dropped serve at 5-2 before breaking back to take the first set in 33 minutes.
Sharapova struggled for more than 10 minutes to hold serve in the third game of the second set, then immediately broke Brianti and went on to take the match.
In a mixed display, Sharapova served seven double faults to Brianti's two, three aces to none, nailed 68 percent of first serves and won 70 percent of first serve points. She also made a host of unforced errors and converted only five of 11 break points.
Third-seeded Russian Svetlana Kuznetsova also advanced to the second round, beating New Zealand wild card Sacha Jones 6-4, 6-2.
Kuznetsova took an early 2-0 lead in the first set, then gave up serve and had to battle hard against the lowly ranked New Zealander.
"She was playing good, aggressive and she had nothing to lose," Kuznetsova said. "There were a lot of things together and that was why I was a little tight, but in the end I loosened up a little bit and I could put more pressure on her."