England, playing their first match of the post-Fabio Capello era, looked to have snatched a draw after goals in the final five minutes from Gary Cahill and Ashley Young cancelled out efforts from Robben and Klaas-Jan Huntelaar.
But just as Young’s injury-time equaliser had sent a 76,283 Wembley crowd into raptures, Holland swept forward and Robben latched onto a Mark van Bommel pass to curl a superb winner beyond Joe Hart.
It was the dramatic final act of a memorable game which had seen England haul themselves back to parity after Holland had appeared to be coasting to victory.
England caretaker manager Stuart Pearce said his youthful side’s “naivety” had been responsible for the defeat.
“We probably showed a little bit of naivety and a slight lack of belief,” Pearce said. “That’s something we’ve got to get into the squad, going forward.
“Once we’d got ourselves back into the game, we’re disappointed to have been beaten. But there were a few good showings, we learned a lot and that was the exercise.”
Dutch coach Bert van Marwijk meanwhile praised his side’s performance as they banished the memory of their last international, a 3-0 defeat to Germany.
“We lost against Germany on the counter-attack and we didn’t want to lose on counter attack here…you have to defend against England as they have a lot of very fast players and that’s a weapon.
“But we were happy to play our football, and the pitch was unbelievably good,” he added.
Earlier, Robben and Huntelaar struck inside the space of a minute to puncture the optimism surrounding Pearce’s squad.
Pearce had named an experimental side, opting for Tottenham’s Scott Parker as captain ahead of Steven Gerrard while handing starts to international novices Danny Welbeck, Chris Smalling, Cahill and Leighton Baines.
But England were exposed early in the second half as the Dutch cut loose with deadly accuracy, Robben and substitute Huntelaar scoring in rapid succession.
Robben drew first blood with a superb individual effort on 57 minutes.
The Bayern Munich winger picked up a stray England pass inside his own half, surged forward and as Cahill and Smalling backed off, fired an unstoppable low shot beyond Hart.
England had barely had time to digest that setback before it was 2-0.
Schalke 04 striker Huntelaar — who had replaced Arsenal’s Robin van Persie at half-time — swept a pass out to Dirk Kuyt on the right flank.
Kuyt returned the compliment with a teasing cross and Huntelaar leapt high to nod past Hart to double Holland’s lead.
The goal came at a cost for both sides, Huntelaar and Smalling being substituted after a sickening clash of heads which left both players needing hospital treatment.
England had their chances to get back in the match, but subsitute Stewart Downing volleyed wide from James Milner’s cross while Daniel Sturridge, who had replaced Gerrard midway through the first half was responsible for a glaring miss late on with the goal at his mercy.
But England did finally get on the scoresheet on 85 minutes when Baines picked out Cahill and the Chelsea defender beat the offside trap to slot past Maarten Stekelenburg.
Then in the first minute of stoppage time, substitute Phil Jones slipped in Young who lifted his shot over Stekelenburg for a scarcely credible equaliser.
England’s joy was short-lived as Robben conjured up another magical finish to give the World Cup finalists a deserved win.
A low key first half had seen England make the brighter start even if genuine goalscoring chances were thin on the ground for the home side.
However in a foreshadowing of what was to come, the best chance of the first half fell to Robben after 14 minutes, the former Chelsea player turning Micah Richards and forcing Hart to save smartly at his near post.
Thereafter England were on top but tellingly never really tested Stekelenburg in the Dutch goal.
Pearce was given cause for alarm after only 33 minutes however when Gerrard, making his first start for England since 2010, was substituted as a precaution to be replaced by Sturridge.
Sturridge however made an instant impact, embarrassing Erik Pieters for pace before firing in a low centre across the face of goal.
Parker meanwhile found himself on the receiving end of a brutal challenge from Kuyt, the Liverpool player taking out the Spurs midfielder with a flying leap that somehow escaped a caution.