The Liverpool midfielder opened the scoring with a 31st-minute header in Minsk and doubled the advantage with a rising thump from distance into the top corner before half-time.
Belarus struck back shortly after the interval but the Dutch held firm for three points, with Wijnaldum and Virgil van Dijk playing the full 90 minutes of the tie.
There was victory for Andy Robertson, too, the Reds left-back captaining Scotland to a 6-0 rout of San Marino in their qualifier at Hampden Park.
Fabinho and Roberto Firmino were both involved as Brazil played out a second successive 1-1 draw in their friendly double-header in Singapore.