The Frenchman, who had been seeded to meet Olympic champion Andy Murray in the quarter-finals, was horribly out of sorts and crashed out 6-4 1-6 6-1 6-3.
Tsonga, a quarter-finalist here last year and a semi-finalist at Wimbledon last month, looked like he had turned things around in the second set but instead Klizan pulled away again in the third.
The Slovakian then opened up a 4-0 lead in the fourth on his way to victory.
Klizan, who is likely to face another Frenchman, 32nd seed Jeremy Chardy, in the next round, was understandably thrilled with his breakthrough victory.
The 23-year-old said: “He’s number six in the world and I beat him. I think it’s my best result in my career and I’m looking forward to playing Saturday in the third round. There is a chance to win again.”
American Mardy Fish, the 23rd seed, became the 10th player to recover from two sets down to win against Russia’s Nikolay Davydenko, a new record for the US Open.
Fish proved the tougher in sweltering conditions in Arthur Ashe Stadium to win 4-6 6-7 (4/7) 6-2 6-1 6-2, while 30th seed Feliciano Lopez beat fellow Spaniard Pablo Andujar 6-4 6-1 6-7 (5/7) 3-6 7-5.
Eleventh seed Nicolas Almagro had to win the final two sets to defeat German Philipp Petzschner 6-3 5-7 5-7 6-4 6-4, while 17th seed Kei Nishikori beat Tim Smyczek of the US 6-2 6-2 6-4.
In the women’s singles, crowd favourite Ana Ivanovic had a comfortable 6-2 6-2 win over Sweden’s Sofia Arvidsson.
The first-round loss for eighth seed Caroline Wozniacki has opened up Ivanovic’s draw and a quarter-final spot looks well within her grasp.
Fellow Serb Jelena Jankovic, whose career has also been on a downward spiral, progressed with a 6-4 6-2 win over Lara Arruabarrena-Vecino, while there were also wins for Dominika Cibulkova and Maria Kirilenko.
Russian Kirilenko, the 14th seed, has been in fine form and beat Hungary’s Greta Arn 6-3 6-2, while 13th seed Cibulkova toughed out a 7-6 (7/3) 7-6 (7/3) victory over Bojana Jovanovski.