Nothing could separate the Frenchmen in the opening four games of the first set as the duo registered two games apiece.
However, Tsonga soon inflicted two breaks of serve en route to a 5-2 lead before securing a first-set advantage.
Mannarino - 80th in the ATP rankings - lost his serve once more in the opening game of the second set before the 28-year-old moved halfway toward the next round by taking a 3-1 lead.
The following four games went with serve as Tsonga took a 5-3 lead to go one game from victory.
Mannarino snatched one game back to reduce the deficit, but it appeared to simply delay the inevitable as the world number 11 held serve to secure a straight-sets win and move into the next round.