Romanian Halep, playing her first match since a semifinal exit at the Australian Open, was rusty in the opening set as Jabeur got off to a flier and the Romanian was visibly frustrated.
However, the world No. 2 bounced back to take the opening three games of the second set and rediscovered her touch from the baseline with powerful groundstrokes that forced Jabeur into errors.
The third set was tight and went to a tiebreak in which Jabeur saved three match points, and created one of her own, before Halep converted her fourth match point to advance to the quarter-finals.
"It was a very tough match, she played really well," Halep said in a post-match interview. "Congrats to her, I was a little bit lucky to win tonight.
"First match after a long time, (it) is tough to play. I gave everything I had, I just wanted to win the match. I didn't give up (on) any point, I'm really proud that I fought till the end."
While Jabeur hit 26 winners to Halep's 10, her unforced error count of 41 and five double faults proved decisive.