Nadal breezed past Jordan Thompson and Corentin Moutet to reach the third round, where the Spaniard had few difficulties on Court Suzanne-Lenglen against world No.29 Van de Zandschulp.
The pair exchanged breaks to begin the match, but the 13-time winner at Roland Garros soon took control as he only lost four points on his service in the first set, all of which came in the first game.
Van de Zandschulp continued to struggle in the second set as Nadal triumphed in a lengthy third game to break again, before following suit in the Dutchman's next service to further his advantage en route to taking a two-set lead.
World No.5 Nadal again opened the third set by battling to break Van de Zandschulp twice and had the opportunity to go 5-0 up with points in hand.
The Dutchman fought back to win three straight games before claiming another, leaving the set finely poised at 5-4 to Nadal.
However, the 35-year-old Nadal regained his composure to wrap up victory and will next face Felix Auger-Aliassime, who defeated Filip Krajinovic.