U.S. coach Tom Sermanni kept his most experienced stars on the bench, but his team had plenty of players ready to step in.
Tobin Heath and Press scored before the break for the Olympic champions, and Press added a third on the hour to bring her international tally to six goals in only seven matches.
The Dutch attacked whenever they got the chance, and it finally paid off in the 81st minute when Manon Melis lobbed Ashlyn Harris to make it 3-1.
Sydney Leroux set up both first-half goals, providing the touch of class the Americans needed to break down a stubborn defense.
The Dutch had earlier twice cleared efforts off their own line, and goalkeeper Loes Geurts tipped over a powerful long-range drive by Yael Averbuch before the team finally succumbed to the relentless pressure.
Abby Wambach stayed on the bench, frustrating her attempt to catch all-time top scorer Mia Hamm's tally of 158 goals. Wambach has 155. Captain Christie Rampone and experienced midfielder Shannon Boxx also started on the bench.
The Americans started their trip to Europe with a 3-3 draw at No. 2-ranked Germany in Offenbach on Friday, conceding two late goals. The win in The Hague extended the U.S. team's unbeaten run to 31 matches.
Sermanni, in his eighth match since taking over the team, made 10 changes to the side that drew with Germany, taking stock of a squad with possibly an eye on World Cup qualifying late next year.
Julie Johnston had a header disallowed for offside in the 72nd minute, before Melis narrowed the lead.
For the first American goal, Leroux went around Kirsten van de Ven and crossed from the right for Press, who laid off the ball for Heath to curl into the corner in the 36th minute for her eighth international goal.
Press made it 2-0 a minute before halftime, running onto a through pass by Leroux and calmly stroking the ball past Geurts from just inside the area for her fifth goal in just seven appearances.
She needed no help for her second, charging through the heart of the Dutch defense -- which lacked captain and central defender Daphne Koster, who hobbled off injured a few minutes earlier -- and driving a low shot into the far corner.
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