Tsonga took a 5-0 lead in the tiebreaker and had two forehand winners to clinch the match.
The 12th-ranked Frenchman, who won the Johannesburg title two weeks ago, leads Djokovic 4-1 in career meetings.
Tsonga made the most of his chances in the first set, converting his only break point at 3-3 when a backhand approach shot from Djokovic caught the tape.
Djokovic wasted five break points in the first set, including three at 0-40 when Tsonga served for the set. Tsonga used three powerful serves to save the three break points, then had an ace and won the set when Djokovic's return sailed long.
Gilles Simon, the 2007 champion, played unseeded Michael Llodra later Saturday.
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