Gauff, the 19-year-old from Florida, went 0-3 in singles at the season-ending championship in 2022.
She quickly grabbed the first seven games against Tunisian Jabeur before play was halted in Cancun, Mexico on Monday night because of the weather. When they resumed, Jabeur held serve but she wouldn't win another game.
"After the rain delay, I was just focused on keeping my foot on the gas pedal," Gauff said.
"I'm just happy ... to finally get a win here in this event."
Gauff, who is seeded third, will face Iga Swiatek in her next match on Wednesday after the Pole climbed out of a deep early hole against Marketa Vondrousova and then pulled away by dominating the second set for a 7-6 (7-3) 6-0 victory.
World No.2 Iga Swiatek made a slow start in Mexico but powered to a first-up two-set triumph.
Swiatek, who won the French Open in June for her third grand slam title, is ranked No.2 and has a chance to overtake Aryna Sabalenka at No.1, depending on their results at the season-ending championships.
Left-handed Czech Vondrousova, the reigning Wimbledon champion, broke in three of Swiatek's initial four service games en route to a 5-2 edge.
Vondrousova served for the set at 5-2 and 5-4, but the the former world No.1 began turning things around and grabbed 13 of 17 points in one stretch.
Both players complained about the court, which has already been criticised by Sabaleka.
Vondrousova wrote on Instagram: "My first WTA Finals is not at all what I imagined. We work hard all year to get to the finals and in the end it's just a disappointment.
"(The) stadium is not at all ready for the matches and to me it feels like the people from WTA are absolutely not interested in how we who are supposed to play on that court feel. We do not feel that anyone listens to us and is interested in our opinions. Very sad."
Swiatek added to the criticism, saying in her on-court interview that the surface was "not comfortable" while she also appealed for more fans to attend the matches.
The WTA said in a statement: "The team has worked diligently on an expedited timeline amid weather challenges to ensure the stadium and court meet our strict performance standards."
In doubles action, No.2 seeds Storm Hunter and Elise Mertens started with a 6-4 6-2 win over Japanese No.3 seeds Shuko Aoyama and Ena Shibahara.
Australian Hunter, who's in contention to finish a career-best year as the world No.1 women's doubles player, and Belgian Mertens, who won WTA 1000 titles in Rome and Guadalajara this season, took 76 minutes to win their first round-robin match of the week.
The combination's record together now improves to 29-10 for the year and they will next face fellow Aussie Ellen Perez and American Nicole Melichar-Martinez.
Perez and Melichar-Martinez are yet to play their opening match, with rain delaying the start of their showdown against fifth-seeds Desirae Krawczyk and Demi Schuurs.
