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Huesler arrived in Montpellier on a high from victories over German duo Alexander Zverev and Oscar Otte for Switzerland in Davis Cup qualifiers last weekend.
The left-hander saw off 18-year-old Frenchman Van Assche 6-3 3-6 6-3 and will get a chance to improve his perfect record against Rune to 3-0.
Italian Lorenzo Sonego sent eighth seed Benjamin Bonzi packing with a 6-4 6-3 win, while French-born American Maxime Cressy progressed with a 6-3 6-2 defeat of Antoine Bellier.
Arthur Rinderknech and Quentin Halys also advanced on home soil, along with Marton Fucsovics and Filip Krajinovic.