Victory over Poland on Friday (AEST) meant the Oranje only needed to avoid a heavy defeat to their neighbours at the Johan Cruijff Arena in Amsterdam to seal top spot in Group A4.
Belgium never looked like they had the firepower to pull off such a result, with Liverpool defender Van Dijk securing three points for the host by scoring in the 73rd minute.
The result meant the Netherlands topped their group with 16 points, with Roberto Martinez's Red Devils six points behind in second.
Belgium looked bright in the early stages, with Eden Hazard blazing over from a promising position and Michy Batshuayi firing at Remko Pasveer after being played in by Kevin De Bruyne.
At the other end, Denzel Dumfries cracked wide from 12 yards after fine work down the left from Vincent Janssen, which was the closest the hosts came in a first half that saw them fail to have an attempt on target.
Dumfries again went close at the start of the second period, while Belgium's Amadou Onana was denied by a smart stop from Pasveer shortly after the hour mark.
Steven Bergwijn powered a shot straight at Thibaut Courtois as the Netherlands cranked up the pressure, before Van Dijk handed the hosts victory with a close-range header from Cody Gakpo's corner.
Courtois did well to deny Davy Klaassen and Bergwijn in the closing stages, while Belgium substitute Dodi Lukebakio struck the post with a sensational overhead kick with almost the last kick of the game.