Holland will now face Mexico in a last-16 clash in Fortaleza on Sunday, after the Central Americans beat Croatia 3-1 to finish as Group A runners-up, while Chile take on hosts Brazil in Belo Horizonte the previous day.
Chile saw more of the ball in the opening 45 minutes on Monday and Felipe Gutierrez twice came close to opening the scoring, blazing a low Alexis Sanchez corner over the bar before heading Marcelo Diaz’s free-kick wide from close range.
Stefan de Vrij squandered Holland’s best first-half chance as he put Arjen Robben’s inviting free-kick wide with a flying header, while Robben himself also threatened as he fired wide following a surging run forward.
The introduction of Depay appeared to open things up for Holland after the break and he forced Claudio Bravo into tipping his long-range effort over the bar for the corner which led to the opening goal.
The deadlock was eventually broken by Fer, who had replaced Wesley Sneijder moments earlier, when he rose to meet Daryl Janmaat’s cross from deep with a towering header.
Holland then wrapped things up in added time when Robben broke from a Chile corner and he found Depay unmarked at the back post to tap in from close range.
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.
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 Sanchez delivered a corner to the feet of 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.
Sneijder struck the resulting free-kick towards the near post but goalkeeper 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 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 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.