Tsonga, the tournament's No. 1 seed, opened quarterfinal play with a 6-4, 7-5 victory over Edouard Roger-Vasselin.
Tsonga had 14 aces and won 70 percent of the points on serve but had to fight off 11 break points. Roger-Vasselin, however, was able to only cash in one such chance.
Del Potro, seeded fourth, took nearly 2 hours to edge past fifth-seeded Richard Gasquet 7-5, 7-6 (7-5). Del Potro, who won 78 points to Gasquet's 77, lost his serve once in each set but managed to hang on in the tiebreaker.
Friday's wins were the 200th in their careers for both Tsonga and del Potro.
The other semifinal Saturday will have No. 3-seeded Janko Tipsarevic playing Michael Llodra.
Tipsarevic capped Friday's play with a 6-4, 6-4 win over seventh-seeded Ivan Ljubicic. Tipsarevic had nine aces and no double faults in winning 71 percent of the points when serving. He didn't face a break point.
Llodra was a 7-6 (7-5), 7-5 victor over Albano Olivetti in a battle of unseeded French players. Llodra lost just five points in 12 serving games.