Despite admitting that he is pleased to have overcome the challenge of Beck, Tsonga has conceded that he lost concentration for parts of the third set.
"I think I played good tennis the first two sets, and after that I lost a bit of concentration at the beginning of the third set," Tsonga told reporters.
"Then I came back, and, you know, I did some effort to come back. It was not easy today because the weather was hot. I'm happy to go through this round really quickly."
The 27-year-old has never gone beyond the quarter-finals at Flushing Meadows.