The pair, playing on Court One, were held up by a rain break early in the third set but played on for nearly three hours after the resumption and Tsonga came through 6-3 3-6 25-23.
Tsonga was serving first and therefore had a big advantage, and he twice held match point - once at 16-15 and again at 21-20 - but both times Raonic came up with huge serves.
The 21-year-old, who is ranked 23rd in the world, is one of the game's rising stars and he held Tsonga at bay until the 48th game of the set.
This time Tsonga created three match points and, although Raonic saved one, on the next point a drop shot was just out of his reach, with the Frenchman smashing the ball away just to be sure and screaming with delight and relief.
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