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.