The top half of the draw is led by Iga Swiatek, who might face Emma Raducanu in the second round.
She won the final seven games after breaking serve four times. In winning, Jabeur scored 25 goals, more than double Haddad Maia's tally of 11.
Iga Swiatek, the current world No. 1, will return in an effort to win her third straight Internazionali BNL d'Italia championship.
Jabeur, a quarterfinalist the past three years in a row and a finalist in Charleston last year, defeated Dolehide in one hour and 21 minutes.
Day 3 of the WTA 500 competition saw the second seed Jabeur make it through to the round of 32 thanks to a comfortable win over Lesia Tsurenko.
Both players had 13 successful swings, but Badosa made fewer unforced errors than Sherif, who had eight.
Iga Swiatek had one of the most successful tennis seasons in history, winning 67 matches and eight tournaments, including two Grand Slams.
The WTA 1000 tournament will have Spanish tennis player and world no. 4 Paula Badosa as the top seed, followed by Aryna Sabalenka and Jessica Pegula.
The Transylvania Open is a WTA 250 tournament and is part of the WTA Tour. The competition is conducted on indoor hardcourts at the BTarena.
Swiatek was forced to drop from the Madrid Open in April due to a shoulder ailment, but she was at her best against Sabalenka on Saturday.