Tsonga was the runner-up at the 2008 Australian Open and a semifinalist at Wimbledon this year. He had reached at least the third round in 18 straight Grand Slam trips.
The 23-year-old Klizan, meanwhile, had failed to make it past the second round in three previous Grand Slam appearances. He had never defeated an opponent ranked better than No. 49.
Earlier Thursday, two players who have struggled to live up to high rankings in the past easily won their matches.
A week before the start of the Open, Ana Ivanovic couldn't walk without pain in her right foot.
"That's when I started to panic a little bit," she said.
Two matches into the tournament, the 2008 French Open champion is feeling healthy and relaxed. The 12th-seeded Ivanovic and another Serbian former top-ranked player, Jelena Jankovic, have quietly reached the third round at Flushing Meadows. Each has dropped just nine games through a pair straight-set wins.
Ivanovic beat 51st-ranked Sofia Arvidsson of Sweden 6-2, 6-2 on Thursday.
Asked if the torn tendon is fully healed, Ivanovic laughed and said, "I still have a handful of pills every morning."
But the foot hasn't been hurting since the tournament started, and Ivanovic's draw is looking fairly painless with Caroline Wozniacki and Francesca Schiavone eliminated in her quarter.
But Ivanovic knows that being the favorite guarantees nothing. In 2008, coming off that title at Roland Garros and at No. 1 in the world, she was stunned by 188th-ranked Julie Coin in the second round here, bothered by a thumb injury. The top-seeded woman had never lost that early in the tournament since the Open era began in 1968.
Ivanovic has been trying to regain her health and her confidence ever since. She has yet to make it back to even a quarterfinal of a Grand Slam event.
"I'm really motivated. I want to get back to the top and back in contention to win Grand Slams again," Ivanovic said. "It's been a long process of getting my mind there and my body and game and everything together. Still, it's going to be a lot of hard work and long process, but I'm starting to enjoy it as well.
"I know if it doesn't happen this week, it's coming."
It's a similar story for Jankovic, who defeated 115th-ranked Lara Arruabarrena-Vecino of Spain 6-4, 6-2 on Thursday. Both women reached No. 1 in the world in 2008, a breakthrough year for Serbian tennis when Ivanovic won the French, countryman Novak Djokovic took the Australian Open, and Jankovic reached the final at Flushing Meadows.
While Djokovic has since won four more Grand Slam titles, Jankovic lost in the first round at Wimbledon this year.
She's seeded 30th this week though, as she noted with a laugh, her ranking is now up to No. 27.
Jankovic could face second-seeded Agnieszka Radwanska, one of the top players on the court later Thursday. No. 1 Roger Federer opens the night session at Arthur Ashe Stadium against 83rd-ranked Bjorn Phau. Then sixth-seeded Angelique Kerber takes on seven-time Grand Slam champion Venus Williams, the juicy second-round match made possible because the American is unseeded after missing time because of illness.
In other women's second-round action Thursday, 13th-seeded Dominika Cibulkova and No. 14 Maria Kirilenko advanced in straight sets.
Kei Nishikori, seeded 17th on the men's side, eliminated American Tim Smyczek. No. 11-seeded Nicolas Almagro needed five sets and 3 hours, 19 minutes to defeat Philipp Petzschner.