The Dutch continued their penchant for strong second-half displays, grabbing both of their goals after the interval.
The opener came in the 77th minute when Leroy Fer, who had only entered the match two minutes prior, nodded home a corner kick. Louis van Gaal's men then tacked on a late insurance goal with Memphis Depay capping a well-worked counter with a simple finish from close range.
The result allows the Netherlands to face the runner-up from Group A, which is likely to be either Mexico or Croatia.
Chile, meanwhile, finishes second in Group B to likely book a meeting with Brazil in the knockout round for the second consecutive World Cup, assuming the Brazilians finish atop Group A.