Wijnaldum was introduced just after the hour, replacing captain Robin van Persie in what looked a massive gamble by coach Guus Hiddink to break the deadlock in their Group A game.
It paid immediate dividends as Wijnaldum squeezed home the opening goal in the 67th minute, followed by a second for Luciano Narsingh four minutes later.
It ensured the Dutch kept alive their hopes of an automatic qualifying berth as they stayed third but narrowed the gap on the top two. They trail Iceland by five points and the Czech Republic by three with each having four games left.
Iceland beat the Czechs 2-1 in Rejkjavik on Friday.
Wijnaldum used his strength to turn with his back to goal and toe-poke home after an initial shot from Wesley Sneijder had been blocked by the Latvia defence.
The goal came after a long period of Dutch dominance, including a first half Sneijder shot that hit the post, amid growing frustration at their inability to break down the home defence.
Van Persie, seeking a 50th international goal, looked unhappy at being taken off but was soon celebrating as the visitors finally broke through.
Narsingh’s goal came in the 71st minute after a defence-splitting pass from Danny Blind caught Latvia's centre backs too high up the field and allowed the winger to run in on goal and expertly slot home.
The victory will come as relief to Hiddink, whose tenure since taking over from Louis van Gaal in August has seen some topsy-turvy performances.
Last week the Dutch lost 4-3 to the United States in a warm-up friendly which led to criticism of their defence.
(Reporting by Mark Gleeson; Editing by Ken Ferris)
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