Schoop's second-inning home run finished off a three-run rally that put the Dutch up 4-0. The pitching took over from there, holding Australia to one run the rest of the way.
The Netherlands improved to 2-1 in Pool B play and will advance to the WBC second round, which begins Friday in Tokyo. Taiwan (2-0) and South Korea (1-1) played later Tuesday to decide which other Pool B team would make the second round. Australia (0-3) is eliminated.
Andrelton Simmons opened the Netherlands' first inning with a double and took third on a sacrifice by Schoop. He made the score 1-0 when Roger Bernadina singled to center.
Simmons knocked in a run on a fielder's choice in the second before Schoop ripped a shot into the seats beyond left field that put the Dutch up 4-0.
Robbie Cordemans (1-0) opened for the Netherlands with five shutout innings. Australia, however, threatened in each of the last three innings. Stefan Welch led off the seventh with a double and Brad Harman knocked him in with a single for the lone Australian run.