Down 5-1 in the third set, Tsonga broke serve twice and then beat Federer in the tiebreaker for a 7-6 (5), 1-6, 7-6 (3) quarterfinal victory.
Del Potro broke Nadal's service twice for a 3-0 lead in the second to set up a 7-6 (5), 6-1 win. Nadal was the defending Rogers Cup champion.
In other quarterfinals, fifth-seeded Andy Roddick recovered from a second-set service break to down Serbia's Novak Djokovic 6-4, 7-6 (4) and will next face del Potro, while third-seeded Andy Murray had a 6-2, 6-4 win over Russian Nikolay Davydenko to set up a clash with Roddick.
Both Federer and Nadal entered the tournament after time off. Federer's wife gave birth to twin daughters while Nadal had 10 weeks off to ease tendinitis in both knees.
"I did not feel real good - 5-1 down and Roger playing well and I had no solutions," said the seventh-seeded Tsonga. "I just told myself 'you have to hit the ball one more time than him' and I did it.
"It's a good thing for me. It's amazing to change this match."
Top-seeded Federer looked to be coasting to a victory when he started struggling on serve just as the Frenchman seemed to find his form.
"It's disappointing but that's what Jo does - he doesn't make a return for an hour and then he puts in a few and than all of a sudden he's back in the match," Federer said. "I should never have allowed it but it happened, so it's a pity."
The Swiss forced a final tiebreaker, but Tsonga used two aces to take the lead and then saw Federer double-fault on match point in the tiebreaker.
"It's a tough match to go through because it was either very close or very one-sided," Federer said. "That doesn't make it easy on the rhythm."
"It's great to get some matches in ahead of Cincinnati (next week) and the U.S. Open," he said. "But my goal wasn't to just to play matches and do press conferences. The whole trip here was to do well and try to win the tournament."
Despite defeat, Nadal was pleased that his knees held up and left encouraged that he is on his way back to top form.
"After two months out of competition it's tough to play at that level - I needed to concentrate more than usual," Nadal said. "The knees were very good.
"I have to be happy with the tournament. (Del Potro) is playing very well and I was at the same level as him in the first set. I thought if I could win the first set I could relax a little in the second and try again in the third, but it was tough."
Asked if he would be back in top shape for the U.S. Open that starts Aug. 31, he said "we'll see."
Roddick's victory was his third this year over Djokovic. The American is unbeaten in tiebreakers in the tournament, extending his lead on the ATP Tour with 33 tiebreaker wins.
"It's been important for me my entire career," said Roddick, the 2003 Rogers Cup champion. "I'm starting to break serve a lot more now, but I certainly grew accustomed to playing a lot of tiebreakers early on. I'm comfortable playing them, and normally I can count on getting a couple of points on my serve."
Roddick is looking to reach a third straight final, after losing to Federer in a five-set thriller at Wimbledon and the loss in Washington.
Murray ended Nikolay Davydenko's 12-match winning streak. Davydenko, seeded eighth, came into the tournament following wins at Hamburg and Umag.
"It will be difficult because Andy is one of the best players this last month," Tsonga said. "I know I have to play my game, stay on the offensive and see what happens.
"I know I have a chance and I will take it."
Figo not planning returnRoddick, del Potro advance toВ D.C. final
