Barbora Krejcikova, the 2021 champion, lost her opening match at the French Open for the second straight year. The 13th-seeded Czech exited the tournament after losing to Lesia Tsurenko of Ukraine 6-2, 6-4.
Gauff, runner-up a year ago, looked uncomfortable early on, with her troublesome forehand frequently letting her down.
World No. 71 Masarova, a former French Open junior champion, took full advantage to dominate the opening set and looked on course for an upset victory.
But Gauff, 19, settled down on a sunlit Court Suzanne Lenglen and reeled off seven games in a row from 1-1 in the second set to take command.
With her confidence restored, Gauff made no mistake as she moved 5-2 ahead in the decider and wrapped up victory with a hold to love as Masarova sent an attempted lob long.
Jabeur, a crowd favorite in Paris, smiled and expressed relief in not repeating last year's mistake, when she lost to Magda Linette of Poland.
"I'm very happy to win my first match on Philippe Chatrier -- because I've never won here," Jabeur said on court about the clay-court tournament's main stadium.
Now she can focus on trying to win her first major. She was runner-up at Wimbledon and the US Open last year.
Jabeur, 28, of Tunisia, has also battled injuries this season. She had knee surgery after the Australian Open and was then sidelined with a calf injury. She had stopped playing against top-ranked Iga Swiatek at the clay-court tournament in Stuttgart, Germany, in late April and then pulled out of the Madrid Open.
"It was a very difficult period for me after Stuttgart," said Jabeur, adding that she's beginning to find her rhythm.
Jabeur struck 27 winners to Bronzetti's seven, though with 24 unforced errors she'll have room to improve.
"I feel 100% fit. I need to have more matches under my belt to gain confidence," she said.
Also Tuesday, 16-year-old Russian Mirra Andreeva had a memorable Grand Slam debut by dominating Alison Riske-Amritraj 6-2, 6-1. Andreeva's older sister -- 18-year-old Erika -- was facing Emma Navarro later in the day.
Reuters and The Associated Press contributed to this report.