Georginio Wijnaldum struck on the stroke of half-time and Memphis Depay chipped home a cheeky stoppage-time penalty to bag a win in Rotterdam for Ronald Koeman's revitalised side that leaves the impressive Dutch needing just a point against relegated Germany on Monday to leapfrog France and make the semi-finals.
The Dutch are a point behind leaders France, who only needed a draw themselves on Friday to qualify for the knockout stage in their last match of the group.
Wijnaldum's goal came practically at the midway point of a match dominated by the hosts, who had the better of the play and chances against the lacklustre world champions.
The closest Deschamps' men came to scoring was a weak 10th-minute header from Antoine Griezmann, who was otherwise anonymous alongside the equally invisible Kylian Mbappe.
The Dutch meanwhile peppered Hugo Lloris' goal from the off, with Wijnaldum forcing the France keeper's first save with just a minute on the clock following an impressive burst from star turn Depay.
The match would have been done and dusted long before the final whistle had it not been for Tottenham stopper Lloris, who engaged in an almost personal battle with the Netherlands' vibrant front three of Depay, Ryan Babel and Steven Bergwijn.
Depay was in particularly fine fettle, and the Lyon attacker was denied three times in the space of three second-half minutes by Lloris to stop the Dutch adding to their total.
First Lloris pushed away Depay's stinging free-kick in the 73rd minute, then two minutes later the Spurs man saved his bamboozled defenders with two smart saves from the striker in a matter of seconds.
France finally creaked into action not long after, but offered little going forward, and with the match rolling into injury time Lloris once again saved his team's blushes with a superb save from Frenkie De Jong's long-range strike following a rapid breakaway.
However De Jong, picked out by Deschamps on Thursday as one to watch for the Netherlands, helped his side seal the points when he was bundled down in the area by Moussa Sissoko with seconds left.
Depay stepped up and capped a brilliant individual and team display by clipping a panenka spot-kick over a despairing Lloris, announcing the return of the Netherlands to the big stage after years in the doldrums.