Van Persie put the Dutch in front after 17 minutes and Narsingh broke through on the counter-attack in stoppage time to seal an 11th successive World Cup qualifying win for the hosts.
The home side's rejigged defence, including 20-year-old Bruno Martins Indi and teenager Jetro Willems, made a shaky start, allowing Omer Toprak to go close with a first-minute header for the visitors.
The goal boosted the home side's confidence but their careless defending continued when Willems lost the ball to Arda Turan, only for the midfielder to shoot wide.
"We should have decided this match earlier as we used the space on their flanks well, but then failed to play it out properly," Dutch coach Louis van Gaal told reporters.
"We played sloppy in possession and some players who didn't reach their normal level, like [Daryl] Janmaat and [Jordy] Clasie, but we always maintained our organisation.
"The chances we gave away were only with corner kicks and personal fouls, but besides that we created more."
