The pair found the net inside the last 15 minutes to settle a largely forgettable encounter in Sao Paulo on Monday and ensure that Louis van Gaal's men will likely avoid host nation Brazil in the last 16.
A meeting of two of the competition's most eye-catching teams had been highly anticipated, yet it had failed to live up to its billing before late heroics from Fer and Depay.
But it was always Van Gaal's men who had looked the most likely to secure victory, with their third successive triumph ultimately coming from two unlikely sources.
Chile, though, can still take solace from having already secured their spot in the knockout phase, where it seems certain Croatia or Mexico await.
The South Americans were beginning to enjoy the better of proceedings and came close to breaking the deadlock when Felipe Gutierrez curled over after being picked out by Alexis Sanchez's clever corner.
But Louis van Gaal's men responded well, enjoying a good spell towards the end of the opening period.
Netherlands' endeavour almost brought reward, too, as Stefan de Vrij headed Arjen Robben's vicious, curling free-kick wide.
Suddenly starting to make his presence felt, Robben illustrated his vast quality when picking up the ball inside his own half before beating two players and shooting narrowly wide.
The game was taking on an end-to-end nature, epitomised by an unmarked Gutierrez back-heading wide from Marcelo Diaz's set-piece.
Robben still looked the likeliest of the Netherlands' attacking players, firing straight at Claudio Bravo after wriggling into space in the box.
Bravo had to be on high alert with 15 minutes to go, turning Depay's 20-yard effort over the crossbar.
Yet he could do little moments later as Fer met Daryl Janmaat's centre with a bullet header that flew into the corner.
