Fer's first international goal on 77 minutes and Depay's strike in injury time brought a rousing finish to a cautious game between two sides who had already reached the knock-outs.
In a match of few chances, Fer buried a strong header with just his second touch after coming on and Depay slid in to meet a raking cross from man-of-the-match Arjen Robben.
"The most clever team won the game," said Netherlands coach Louis van Gaal, although he dismissed his goal-scoring substitutions as "luck".
"Leroy Fer... I know he's really good at headers, that way you have a head-start against Chile, you have an advantage," Van Gaal said.
"With Memphis, we analysed that Chile in the last 15 minutes always give more space so if you field a more creative player you'll have a chance to make opportunities."
The Netherlands and Chile were level on points before their game in Sao Paulo but top place was crucial to hopes of avoiding Brazil, who are expected to win Group A, in the last 16.
"We did everything possible but the Netherlands imposed their play on our attackers through their defence. We need to polish a few things," said Chile coach Jorge Sampaoli.
Both started cautiously in bright sun at a packed and noisy Corinthians Arena in Sao Paulo.
With Robin van Persie suspended, Dynamo Kiev's Jeremain Lens made his World Cup debut up front for the Dutch and Fenerbahce veteran Dirk Kuyt was deployed on the left of midfield.
Chile benched Juventus's Arturo Vidal, who was one booking away from suspension, but took a chance on fit-again midfielder Charles Aranguiz, who was also on a yellow.
A slip by Barcelona's Alexis Sanchez let Chile's first dangerous moment go begging when Aranguiz's dummy surprised him on the edge of the box.
The Netherlands' best early moment came when Wesley Sneijder had a long-distance free-kick parried by Claudio Bravo at his near post.
A moment of magic nearly put the Dutch ahead when on 40 minutes, Sneijder won the ball from Marcelo Diaz and fed Robben, who shrugged off Gonzalo Jara and charged forward.
As Chilean defenders backed off, the Bayern Munich forward rode Gary Medel's challenge and surged into the box but with space to shoot, he dragged his effort wide.
Chile nearly took the lead a minute before half-time when Felipe Gutierrez rose to meet Diaz's free-kick from deep and nodded a back-header narrowly wide.
Just after the hour-mark, Sanchez had a penalty shout turned down by Gambian referee Bakary Gassama.
Sanchez then nutmegged Lens on the byline and warmed goalkeeper Jasper Cillessen's hands with a shot from a tight angle as the tempo and noise-level rose.
Lens came off for PSV Eindhoven's 20-year-old forward Depay, who scored the winner against Australia, and Sneijder withdrew for Norwich City midfielder Fer.
And just two minutes after coming on, the 24-year-old met Daryl Janmaat's high cross from the right with a huge leap and planted an unstoppable header inside the post.
Chile pressed for the equaliser and during a sequence of corners, Sanchez had another penalty shout waved away following a tangle with Dutch enforcer Nigel De Jong.
But as Chile pushed forward, Robben galloped into space on the left and his cross from near the byline was met by the sliding Depay to make sure of an ultimately deserved win.
In Curitiba, Spain ended their miserable World Cup defence with a 3-0 win over Australia.
David Villa became the fourth Spanish player to score in three World Cups when he backheeled home Juanfran's low cross for his 59th international goal in his 97th and final appearance as Spain finally got a win.
Andres Iniesta marked his 100th cap for his country with a lovely through-ball for Fernando Torres to double Spain's advantage on 69 minutes, before Juan Mata slotted home a third eight minutes from time.
Victory means Spain finished third in Group B behind the Netherlands and Chile, whilst Australia slipped to a third consecutive defeat.