'I played great. I'm happy to go through this far.'
Tsonga confessed that he has dropped a few kilograms in recent months as he works on fitness, which showed as he displayed his powerful game against Nieminen in one and three-quarter hours.
Croatian 16th seed Marin Cilic staged a career-fist comeback from two sets to love down, overhauling US player Jesse Levine 4-6, 2-6, 6-0, 6-3, 6-0.
2003 New York finalist Juan Carlos Ferrero performed a similar feat as he came back to oust German Philipp Petzschner 1-6, 3-6, 6-4, 6-2, 6-4.
Second-seeded women's holder Serena Williams had to win a lengthy 11th game of the second set lasting seven deuces to overcome Maria Jose Martinez Sanchez 6-3, 7-5.
The pair have a history from the French Open, when Williams accused the Spaniard of cheating during their third-round match. But no boilovers occurred in New York.
'You can never underestimate anyone. Some people, some days they have great days,' said Williams. 'I was just happy to keep getting through my match.
'I just go and look at every opponent as the best player in the world. I just kept fighting, and every time I had a break point I felt like I had a chance to win one of them.'
Russian Vera Zvonareva beat compatriot Elena Vesnina 6-2, 6-4 while veteran Italian Francesca Schiavone upset eighth seed Victoria Azarenka 4-6, 6-2, 6-2.
Tenth seed Flavia Pennetta of Italy crushed Canada's Aleksandra Wozniak 6-1, 6-1, while Daniela Hantuchova ended the upset run of Vania King 6-2, 6-2 after the Us player had beaten 15th seed Samantha Stosur in the previous round.