HOLLAND 2 CHILE 0
Memphis Depay
Fer headed the ball in from Darryl Janmaat's cross in the 77th minute - less than two minutes after the Norwich midfielder had come on.
Depay then got his second goal in two matches, finishing a Dutch break by converting Arjen Robben's tee-up from close-range in stoppage time to wrap up another three points for Louis van Gaal's men and their 100 per cent record in the group.
After each winning their first two group matches, both sides had already qualified for the last 16 ahead of this contest.
But they went into it with some incentive, knowing that clinching first place in the pool would see them avoid a meeting in the next round with the winners of Group A - likely to be hosts and tournament favourites Brazil, who were in action later on Monday.
Goal difference meant Holland needed only a draw to ensure they remained at the summit and it was the Chileans who showed more attacking intent in the early stages, albeit without truly threatening the Dutch goal.
Eduardo Vargas headed wide and Charles Aranguiz's dangerous ball was cleared by Ron Vlaar before Alexis Sanchez delivered a corner to the feet of Felipe Gutierrez, who sent his shot off-target.
Holland's first real attempt came in the 26th minute after Franciso Silva picked up a booking for a foul on Jeremain Lens, who was in the Oranje side as a replacement for the suspended Robin van Persie. Wesley Sneijder struck the resulting free-kick towards the near post but goalkeeper Claudio Bravo had it covered.
Daley Blind made a sliding challenge in the Holland area on Aranguiz, prompting some calls for a penalty from the stands, but play continued and the Dutch then went close as Stefan de Vrij sent Robben's wonderfully-delivered free-kick wide with a diving header.
Robben, one of the competition's stand-out performers to date, looked to be growing into the game and after another Chile penalty claim went unheeded - this time with Sanchez appealing he had been pushed by Dirk Kuyt - the Bayern Munich man surged from the halfway line to the box, evading a couple of challenges along the way, before sending a shot across the face of Bravo's goal.
Vargas was next to go down in the Dutch area following contact from Vlaar, with nothing being given once again, and Chile then passed up their best opportunity yet just prior to the interval as Gutierrez was presented with a free header from Marcelo Diaz's free-kick but diverted it the wrong side of the post.
The match continued to struggle to really spark into life after the break, with Sanchez lashing an early effort too high.
The Barcelona playmaker was then sent tumbling in the box by the outrushing Dutch goalkeeper Jasper Cillessen but referee Bakary Gassama was again unmoved, although Blind was subsequently booked for bringing the same man down.
Sanchez then outwitted Lens in the box and fired in a shot from a tight angle which Cillessen parried, before Robben's relatively tame effort was dealt with by Bravo at the other end.
Kuyt headed a Robben corner wide with just over a quarter of an hour to go as Holland looked to increase the pressure and Depay then unleashed a shot from outside the box that Bravo stretched to tip over the bar.
Moments later the Dutch made the breakthrough as Robben's corner was collected by Janmaat and his delivery came to Fer, who had the space to power a header past Bravo.
There were further moments of possible contention in the Holland area, with the ball appearing to strike De Vrij's arm on the line and Sanchez again going down, this time under a Nigel de Jong challenge.
Gassama was unmoved again, though, and Chile were then caught on the counter-attack in the last few seconds as the ball came to Robben and his pass was prodded in by Depay in the six-yard box.