Raonic, who lost last year's final to Roger Federer and also needed a tiebreaker to get past Australian qualifier Alexei Popyrin on Tuesday, hit 24 aces to beat Tsonga in 2 hours, 27 minutes.
The sixth-seeded Canadian next faces Marton Fucsovics of Hungary, who beat fourth-seeded Georgian Nikoloz Basilashvili 7-6 (4), 2-6, 7-5.
Also Wednesday, Lucas Pouille upset third-seeded Daniil Medvedev 7-6 (6), 4-6, 6-2, and Germany's Jan-Lennard Struff eased to a 6-2, 6-2 win over Miomir Kecmanovic of Serbia.
Rain delayed the start of play for 3½ hours at the grass-court tournament.
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