Eighth seed Fish, the revelation of the season, had looked the favourite after dominating the third set but a break of serve in the ninth game of the fourth turned the match in Tsonga's favour.
The American received raucous backing from the crowd on Arthur Ashe Stadium but, after treatment for a groin problem, he was unable to handle the raw power of Tsonga.
In the last eight the Frenchman is likely to meet third seed Roger Federer, who he has beaten in their last two matches, including coming back from two sets to love down in the quarter-finals at Wimbledon.
Tsonga felt his physical and mental strength pulled him through and compared the victory to beating the likes of Federer and Rafael Nadal.
The 11th seed said: "Today [Monday] was just really difficult because of Mardy, because of the wind, because of all the conditions. And I just did a great job today [Monday].
"I was mentally strong. And I'm just happy to win because a few years ago it was tough for me to play in these conditions. And today [Monday] I was really, really strong in my head, so I'm happy.
"I just feel good physically. And when you feel good physically, you feel good in your head, and then, even if you are two sets down, or two sets to one down, you know you can win in five sets.
"For me to beat Mardy here, of course it's special because this is the first time I will join the quarter-finals here. And, for me, it's like beating Federer somewhere or Nadal, because he's at home and he wants to do great and play his best tennis here."
If it is Federer he faces next, Tsonga will take a lot of confidence from his victories at Wimbledon and in Montreal, but he is certainly not taking anything for granted.
"It's good to have some wins against him because now Roger knows I'm able to beat him," added the Frenchman. "But every day it's another day.
"Even if I won two times, I know the third time will be difficult - maybe more than the others - because of that, because Roger knows I can beat him and he will do everything to win this time."
Fish was facing Tsonga for the first time, and he had no complaints about the result or his contribution to the match.
The 29-year-old said: "I can look myself in the mirror. I can sleep pretty well nowadays knowing that I'm doing everything I can possible.
"Some matches go my way and some don't. A lot of them have this summer and a few haven't. This is one of them.
"Yes, it's disappointing, no doubt about it. He's a great player. It's not a bad loss. But I was in a good position to win that match."