His victory set up an all-French final on Sunday against Lucas Pouille, who beat another Frenchman Richard Gasquet 7-5 6-3 in the other last-four match.
Second seed Tsonga lost his way in the second set against Kyrgios but recovered to break once in the decider.
The 31-year-old Tsonga saved five of eight break points and had to prevail in the face of 16 aces from Kyrgios to win their first meeting and give himself the chance of a third Marseille crown after his victories in 2009 and 2013.
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(Reporting by Martyn Herman and Ian Chadband, Editing by Ed Osmond)
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