Sijsling, who lost in the doubles final of the Australian Open, used a powerful serve and volley game to beat the third-seeded Tsonga.
Neither player lost a serve in the first set, with the 77th-ranked Sijsling easily winning the tiebreaker.
Sijsling had two break points at 4-3 in the second set, but wasted them both with forehand errors to allow Tsonga to even the match at 4-4. Tsonga then broke Sijsling in the next game and served out for the set.
Sijsling said he suffered "a mental dip" after that, but managed to rally himself for the final set, breaking Tsonga in the 10th game for the win.
He called it "maybe the greatest" victory of his career, "at home, against a top-10 player, in front of this crowd."
Fifth-seeded Gilles Simon beat Belgian qualifier Daniel Brands 7-6 (3), 6-4 despite struggling with his serve in the first set on the indoor hardcourt at Ahoy arena. The Frenchman broke Brands once to take the second set and wrap up the match in 92 minutes.
In the tournament's first upset, Romania's Victor Hanescu beat seventh-seeded Jerzy Janowicz of Poland 7-6 (4), 6-3, while Bernard Tomic of Australia lost a hard-fought first round-match to Bulgarian Grigor Dimitrov 6-3, 3-6, 6-3.
Roger Federer opens the defense of his ABN AMRO title on Wednesday.