The 22-year-old entered the tournament as a qualifier but served well all week to claim victory in s'Hertogenbosch.
She hit eight aces and won 27 of 28 points on her first serve in Saturday's comfortable 6-2 6-4 triumph that took just 70 minutes to compile.
Vandeweghe's only previous final experience came at Stanford in 2012 but she never looked overawed by the occasion.
Instead it was the experienced Zheng who wilted, as she was broken in two of her first three service games.
That saw Vandeweghe take a 4-1 lead and she never looked back in a one-sided first set.
Zheng responded in the second set but again Vandeweghe was too powerful on serve, not allowing her opponent a break point.
And that meant that Vandeweghe's sole break – in the third game of the set – proved enough as she served out to love to claim a memorable victory.
The victory gives Vandeweghe momentum ahead of Wimbledon, which she begins with a clash against 27th seed Garbine Muguruza.
Zheng starts against German Annika Beck but could face 11th seed Ana Ivanovic in the second round.