The match featured only one break of serve and 19 aces as 2009 champion Tsonga prevailed 6-3 7-6 (10/8) in 91 minutes.
Nicolas Almagro also progressed, the Spanish sixth seed beating German qualifier Benjamin Becker in successive tie-breaks, 7-6 (7/4) 7-6 (7/3).
Becker's compatriot Daniel Brands was also beaten as Ukraine's Alexander Dolgopolov won 6-3 6-1.
Jarkko Nieminen eased past Juan Monaco in straight sets in the day's last match.
Nieminen won successive points on Monaco's serve to clinch the first set on a tie-break, then broke in the first game of the second and went on to wrap up a 7-6 (7/4) 6-1 win.