Top seed and title holder Tsonga beat American Jesse Levine 6-3 6-4, his opponent breaking just once as the Le Mans-born world number seven produced seven aces.
Earlier, Monfils recovered from a set down to beat Philipp Kohlschreiber.
The agile Parisian emerged a 6-7 (7/3) 6-4 6-4 winner after battling against second seed Kohlschreiber for just under two-and-a-half hours.
Fifth seed Andreas Seppi of Italy faces Monfils in the semi-finals after defeating Germany's Florian Mayer 7-5 6-2 in just over an hour.
Tsonga awaited the winner of the late-night clash between Nikolay Davydenko and Ivo Karlovic.
And it was Russian Davydenko who came through against the Croatian, the match pivoting on the outcome of a long second-set tie-break.
Karlovic had taken the opening set, but offered little resistance once Davydenko drew level and the 31-year-old beat the man two years his senior 6-7 (7/5) 7-6 (10/8) 6-0.