The 25th-ranked Pouille had not won a set against Tsonga in their two previous matches, which included the final in Marseille in February.
"I am very happy. It has been a great week for me," Pouille said. "Of course, when you play Jo, you expect a very tough match but I am very happy with the way I played."
His victory at the indoor hard-court event made Pouille the only player on the tour this year to win on all three surfaces, after earlier triumphs on clay (Budapest) and grass (Stuttgart).
The 15th-ranked Tsonga, who won in Antwerp last week, went 4-1 in finals this season. It was his third final in Vienna after winning the event in 2011 and losing last year's final to Andy Murray.
Despite Sunday's defeat, Tsonga continued his late quest for an ATP World Tour Finals berth, trailing Pablo Carreno Busta by 295 points for the eighth and final spot.
Pouille controlled the match after saving a break point at 1-1. He won five straight games to take the opening set. He used one more break in the second and closed out the victory when Tsonga hit a return long.