The Frenchman, who is one of the six players competing for four remaining spots at the Barclays ATP World Tour Finals in London, was outplayed in the second set but recovered to win 7-5 1-6 6-3.
Tsonga, the champion in 2011, next meets local wild card Dominic Thiem, who thrashed lucky loser Jaroslav Pospisil 6-1 6-1.
Second seed Tommy Haas ended the run of qualifier Miloslav Mecir in a tight match.
Mecir, the son of the 1988 Olympic gold medallist of the same name, pushed the German all the way but Haas prevailed 7-5 7-6 (10/8).
Third seed Fabio Fognini also won, 7-5 6-2 against Lukasz Kubot, but Philipp Kohlschreiber and Vasek Pospisil were both knocked out.
Fourth seed Kohlschreiber went down 4-6 6-1 7-6 (7/0) to qualifier Ruben Bemelmans while Canadian seventh seed Pospisil also lost in three sets to Dutchman Robin Haase.