Team SD Worx–Protime's Lorena Wiebes finished second ahead of her Dutch compatriot Marianne Vos of Visma–Lease a Bike.
Kool leads the General classification ahead of Anniina Ahtosalo and Wiebes.
"We were a bit far, but I tried to stay calm," Kool told reporters. "I launched my sprint, and it was enough.
"We were in control the whole day. It was a hectic course, but I like it.
"Dreams come true quite fast these days. First yesterday (in the yellow jersey), now today. I guess I'm stronger than ever, I didn't expect this."
Stage three is a 6.3km time trial in Rotterdam.