The first five games were tightly contested and took 35 minutes to complete, with Levine saving seven break points before the top-seeded Tsonga broke back and held for 3-2.
"I had to be fully focused because Jesse was in good shape," Tsonga said. "I'm happy with how I played and happy to reach the semifinals, even though I'm still making a few mistakes."
In the other quarterfinals, fifth-seeded Andreas Seppi of Italy beat fourth-seeded Florian Mayer of Germany 7-5, 6-2, and seventh-seeded Gael Monfils of France topped second-seeded. Philipp Kohlschreiber of Germany 6-7 (3), 6-4, 6-4.
Monfils is returning from a knee injury.
"I'm feeling the strain, but I want to rise above the tiredness and the pain," Monfils said. "I'm surprising myself. I didn't expect to hold out for this long."