World number nine Jabeur broke the 72nd-ranked Tauson's service in a tight third game and nearly dropped her own right afterwards in a marathon 26-point game but held firm and went on to clinch the first set.
With a superb passing shot, the Tunisian immediately took the lead in the second set but could not hold it and had to wait until the fifth game to break again as Tauson hit two mistimed unforced errors.
Tauson, who defeated 2017 Roland Garros champion Jelena Ostapenko in the second round and former runner-up Sofia Kenin in the third, nearly drew level in the 10th game but Jabeur kept the upper hand to wrap up victory in little over an hour and a half.
Jabeur waved her arms and bounced up and down while singing along with fans during her post-match interview on court, later saying that the song was a mix of Arabic, French and Italian that she loosely translated as "it's incredible, step by step to the final".
Jabeur, targeting a first Grand Slam title after finishing runner-up twice at Wimbledon and at the US Open last year, will face world number three Coco Gauff in the quarter-finals.
"It's going to be difficult. She's such a fighter," Jabeur said of the American. "I know I can bother her also but it's going to be a great match."
