Tsonga was unable to seize the initiative early on as Malisse kept pace with the sixth seed, and the pair could not be separated until 5-5 in the opening set.
The Frenchman found the elusive breakthrough at the business end of the set, however, and secured the crucial break of serve to take it 7-5.
Tsonga was again forced to battle his way through another hard-fought set as he took the second with it having been locked at 5-5 with a solitary break of serve.
The sixth seed will next take on Philipp Kohlschreiber of Germany, who defeated Federico Gil 6-2 7-5 in their second-round match.
Tipsarevic will next face 18th seed Alexandr Dolgopolov, with the Ukrainian having beaten Antonio Veic 6-4 7-5 in their encounter.
Florian Mayer beat Ivan Dodig 6-4 7-5 to set up a third-round clash with either John Isner. American Isner maintained his great run of form, which has included a win over world number one Novak Djokovic, by defeating Russian Nikolay Davydenko 2-6 6-3 6-4, highlighted by 10 aces.
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