First-half goals from Memphis Depay (10) and Daley Blind (45+1), swept home in similar fashion from Dumfries crosses, put the Dutch in control but USA forced both the Inter Milan defender and Cody Gakpo to clear off the line before Haji Wright produced an "impossible" 76th-minute finish to set up a big finale.
Standout performer Dumfries ended their hopes of a dramatic turnaround, though, volleying in Blind's cross in the 83rd minute to secure the victory.
USA had been boosted by Christian Pulisic being passed fit to play but the Chelsea forward wasted a glorious opening just three minutes in, shooting at Andries Noppert when clean through.
Netherlands boss Louis van Gaal has lost none of his 11 World Cup games in charge (W8 D3), the outright most for a manager without ever losing in the competition. Only Felipe Scolari (12) has had a longer unbeaten start as a manager in World Cup history than van Gaal (11).
As for the Netherlands - into the last eight for the fifth time in their last six World Cups - they will now turn their attentions to facing the winner of Argentina vs Australia at the Lusail Iconic Stadium at 7pm on Friday December 9.
US on the other hand will something to build on after getting out of the group stages here, but there will also be disappointment at the sense of a missed opportunity. They will depart Qatar and start their preparations for the Fifa World Cup 2026, which they will jointly host with Canada and Mexico.