Tsonga, who won the event in 2009, defeated French countryman Nicolas Mahut 6-3, 6-2 in less than an hour. Tsonga had 10 aces and lost just five points in nine service games.
Mahut won a healthy 57 percent of the points on serve but Tsonga was able to finish off all three of his break-point chances.
Tipsarevic handled David Goffin 6-4, 6-2 by saving all six of the break points he faced. He had two breaks and won half the points off Goffin's serve in the second set.
The first round was wrapped up Wednesday as sixth-seeded Alexandr Dolgopolov got past Lukas Rosol 2-6, 7-6 (7-1), 6-3 and Michael Llodra edged Marco Chiudinelli 7-6, (7-2), 7-6 (7-3) in a 2-hour match.
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