The Frenchman's 6-7 6-3 6-4 win also kept him on course for a place in the season-ending World Tour finals in London next month, moving him to seventh place in the 2011 rankings ahead of Mardy Fish.
Top-seeded Tsonga crashed 25 aces on his way to a first win in four meetings over the former US Open champion, who has been fighting his way back to form after being plagued by a wrist injury last year.
"That was really tough," said Tsonga. "Juan Martin played very well.
"I lost a little motivation after losing the first set but fortunately I got it back quickly." Neither player managed to break serve in the first set and, having fought back from a break point down in the tiebreak, Tsonga then served a double fault to hand Del Potro the opportunity.
The Argentine duly took it when Tsonga over-hit a forehand.
Del Potro appeared to be heading for a win when he broke in the third game of the second set, but Tsonga replied in the next game in what appeared to be the turning point of the match.
The Frenchman broke again in the sixth game when, having missed one break point, he was handed another by a Del Potro double fault and gleefully seized it with a stunning forehand drive down the line.
In the third set, the 26-year-old served nine aces and broke in the seventh game to claim his second ATP title of the year following his win in Metz.
