Neither player faced a break point in the first set, but Kim saved two in the second as Tsonga started to get on top.
Kim missed his chance to level the match as Tsonga, the 2008 Australian Open finalist, rallied from 5-3 down in the second set tiebreaker.
"My tennis wasn't all there, but the desire was there," Tsonga told French television. "When I stepped onto the court I knew I was not going to play well. I just played enough tennis to win."
Third-seeded Ivan Ljubicic of Croatia also progressed after beating Martin Vassallo Arguello of Argentina 6-3, 6-4.
Ljubicic, looking for his first title this season, won 29 of 33 points on first serve including seven aces. The defeat would have been heavier for Vassallo Arguello if he hadn't saved 10 of 12 break points.
Seventh-seeded Benjamin Becker of Germany beat Paolo Lorenzi of Italy 6-2, 6-2, while No. 8 Albert Montanes of Spain topped Fabrice Santoro 6-4, 6-4. The 36-year-old Frenchman is playing his final season on the ATP circuit.
Also, David Guez of France beat Rajeev Ram of the United States 6-2, 6-4, and Marc Gicquel downed Jerome Haehnel 6-1, 6-4 in an all-French match.
Gicquel, runner-up in 2006 and 2007 at the indoor hard-court tournament, saved the only break point he faced. He next plays either sixth-seeded Paul-Henri Mathieu of France or Leonardo Mayer of Argentina.
Michael Llodra of France defeated Lamine Ouahab of Algeria 6-1, 6-2; Kevin Anderson of South Africa beat Simon Greul of Germany 6-4, 4-6, 7-6 (3), and France's Arnaud Clement defeated Spanish player Oscar Hernandez 6-1, 6-3.
Henry blow for BarcaTop-seeded Pennetta beats Shaughnessy in Linz
