Czech player Marie Bouzkova and Spaniard Sara Sorribes Tormo provided stiff competition but eventually succumbed 2-6 6-3 13-11 as Williams grew in belief.
This was the first competitive match for 40 year-old Williams since abandoning her Wimbledon first-round clash against Aliaksandra Sasnovich last June, due to an ankle injury.
It was also her first doubles main-draw match on grass since she and sister Venus won the 2016 Wimbledon title, so she was understandably rusty in the early stages, while world number three Jabeur's nervousness about playing with Williams, which she spoke of after the match, was also evident.
Williams will be on a wildcard at Wimbledon next week, due to her ranking plummeting, as she chases what would be a record-equalling 24th grand slam singles title.
Her game looked sketchy early on, with a smash into the net handing over the second game, before she then blazed a volley over the baseline to concede the early break.
Her own serve was broken as Sorribes Tormo and Bouzkova snatched a 4-1 double-break lead in the opener, which they soon wrapped up.
Williams lost her footing on the grass midway through the second set, slipping over, but she was soon back up, with the contest becoming increasingly competitive.
Jabeur and Williams forged a 4-3 lead in the second set and then broke to force the match tie-break.
All-out assault from Williams brought up a first match point, but the American then rattled a backhand long after Jabeur failed to put away a volley at the net early in the rally.
Another match point slipped away as Jabeur netted from another great chance, but a drop shot from the Tunisian brought up a third, and this time Sorribes Tormo volleyed wide to herald a scream of delight from Williams.
"Oh my god, it was so fun to play with Ons," said Williams. "Our opponents played amazing. They played so well in that first set, they were jamming.
"We were just trying to stay in there after the first set, it was good though.
"I caught some fire behind me, so that's good; I needed that."