Del Potro, the top seed at the weekend event, gutted out a 7-6 (7-2), 6-4 victory over third-seeded Stanislas Wawrinka of Switzerland.
The Argentine will be seeking his second title of the year in his third finals appearance. He racked up his 10th career championship earlier in Marseille while settling for runner-up in Rotterdam.
Second-seeded Gasquet, meanwhile, rallied to best No. 4 seed Albert Ramos of Spain 2-6, 7-6 (7-1), 7-5 in Saturday's other semifinal.
He'll be looking for his seventh career championship and first since 2010, but is 1-3 lifetime against Del Potro.