The Oranje knew a win would lift them above both Germany and their opponents, yet they fell behind in the 75th minute when substitute Josh Magennis headed in Stuart Dallas' cross completely against the run of play.
However, Depay levelled 10 minutes from time and De Jong, brought on shortly after his team fell behind, prodded in on the line in the first minute of stoppage time after his initial effort had looped into the air.
Depay rolled in Netherlands' third - and his sixth of the campaign – to leave Northern Ireland with a huge task to claim a top-two finish in their Euro 2020 qualifying group, with November fixtures against Germany and Ronald Koeman's side still to come.
Netherlands had won 16 successive games at De Kuip but did not look at home during a first half when they managed just one shot on target, via Georginio Wijnaldum's back, which Bailey Peacock-Farrell was equal to.
Northern Ireland's ploy to slow the game down was evident to referee Benoit Bastien, who warned Shane Ferguson for time-wasting less than 60 seconds after the restart and booked Peacock-Farrell with 53 minutes gone for the same offence.
The frustration prompted Koeman to make a double change - Donyell Malen and Donny van de Beek introduced in the 66th minute - with Peacock-Farrell denying Steven Bergwijn and Jonny Evans hooking clear a Wijnaldum effort.
However, having not threatened Jasper Cillessen's goal in the opening 75 minutes, Northern Ireland remarkably went ahead. Both Matthijs de Ligt and Daley Blind failed to clear the lines and Dallas stood up a cross that substitute Magennis reached before De Ligt to head home.
Depay went straight down the other end and forced Peacock-Farrell into an unconvincing save, but the Lyon forward was not denied 10 minutes from time when he collected Malen's cross and rolled a smart finish between Evans' legs and into the net.
An unmarked Malen then headed over but De Jong found the net in stoppage time, prodding over from on the line at the second attempt to convert a deflected Bergwijn cross.
Depay added a third after a good run by Frenkie de Jong to leave Netherlands, Germany and Northern Ireland all on 12 points in the table.
What does it mean? Netherlands and Germany on course for top-two finish
Northern Ireland collected maximum points from their first four games against Estonia and Belarus, but they knew they likely needed to take a further four points from their last quartet of fixtures against Netherlands and Germany.
They were on course for three of those with 10 minutes remaining in Rotterdam, yet the Oranje's late goals mean both they and Germany are set to secure Group C's top two spots.
Depay the guy once again
Forward Depay has now firmly established himself as Netherlands' talisman with six goals in qualifying. The home team struggled to conjure up anything before falling behind, but Depay stepped up when his country needed him the most.
De Ligt not at the races
Netherlands' defence had little to do, but on one of the few occasions the ball entered their box, the defending was dire. Juventus centre-back De Ligt sliced Ferguson's cross straight into the air at first and then allowed himself to get bullied in the air by Magennis to continue a poor start to the campaign for club and country.
Key Opta Facts
- Depay has been directly involved in more goals in Euro 2020 qualifying than any other player (12 – six goals & six assists).
- Since Koeman's first game in charge of Netherlands in March 2018, Depay has been directly involved in 21 goals in just 17 appearances for his country (11 goals & 10 assists).
- Magennis has scored three goals in Euro 2020 qualifiers for Northern Ireland, with all three strikes coming as a substitute.
- Northern Ireland have won just one of their seven encounters against Netherlands in all competitions (W1 D2 L4), losing each of the last three.
Northern Ireland visit the Czech Republic for a friendly on Monday before rounding out the group with a home game against Netherlands and a trip to Germany in November. Either side of that visit to Belfast, Koeman's team face Belarus and Estonia.