The French world number 17 was made to fight for the opening set at London's Hurlingham Club, but stepped up a gear in the second to claim a 7-6 6-3 win in the exhibition match.
Tsonga has been seeded 14th for Wimbledon, while Nishikori has been ranked 10th for the grass-court showpiece.
The All England Club's defending champion makes an appearance at the Hurlingham Club on Thursday, facing off against Spain's Tommy Robredo.
Fellow former winner Rafael Nadal will then be in action on Friday against the same opponent, while Tomas Berdych meets Grigor Dimitrov and Nishikori over the coming days.
Nadal and Murray are seeded second and third respectively for Wimbledon, with Berdych occupying sixth spot.