The Oranje cruised through with a game to spare on Thursday after Memphis Depay opened the scoring at Johan Cruyff ArenA with an early penalty.
Dumfries opened his international account with a late winner in a 3-2 victory against Ukraine on Sunday and the impressive wing-back sealed all three points again in Amsterdam.
Frank de Boer's side were a cut above a poor Austria side and will face one of the third-placed finishers at the Puskas Arena in Budapest a week on Sunday for a place in the quarter-finals.
Austria must regroup ahead of a final group game against Ukraine, with second place up for grabs.
The Oranje were in front just 11 minutes in, referee Orel Grinfeld pointing to the spot after taking a second look at David Alaba's rash challenge on Dumfries. Depay found the bottom-left corner from 12 yards after a short run-up.
Austria were vulnerable under pressure from the Netherlands high press and Depay fired into the side-netting after a mistake from Austria captain Alaba.
Depay wasted a glorious chance to add a second goal five minutes before the break, prodding high and wide with his left foot from close range after Wout Weghorst unselfishly set him up.
Austria tried to pose more questions after the break, but the Netherlands remained much the better side and ought to have been two goals to the good just after the hour mark.
Weghorst's header from a corner was nodded towards goal by Stefan de Vrij from point-blank range and Daniel Bachmann palmed into the path of the fit-again Matthijs de Ligt, who failed to convert the rebound.
The second goal finally arrived midway through the second half, though, Donyell Malen racing clear and drawing out Bachmann before setting up Dumfries for a tap-in.
Alaba flashed a venomous long-range drive wide and Karim Onisiwo should have done better with a header on an evening to forget for Austria.