Kool, born in North Holland, took the yellow jersey on home soil as the women's Tour got underway in the Netherlands with a 123-kilometre flat ride from Rotterdam to The Hague.
Topping 60 km/h as she crossed the line, the dsm-Firmenich PostNL rider claimed her maiden Tour win with an unstoppable surge in the last 100 metres to complete the stage in a time of two hours 47 minutes and 40 seconds.
Finland's Anniina Ahtosalo of Uno-X and Italian Elisa Balsamo of Lidl Trek completed the podium.
"It's unbelievable, it's a dream coming true. It was not an easy season, but this is what it is all about," Kool said.
"It was really hectic, but I liked it. So, I kept on thinking - I like hectic, I like chaos. I went so early and I thought it's too long and it hurt so bad, but it was enough in the end, so no words."
There was drama with 69 km still to go when a mass crash in the middle of the peloton brought dozens of riders to a halt on a bridge near the Meuse River.
Thankfully none of the competitors were seriously hurt and all were able to remount their bikes and take off again in pursuit of the front half of the peloton.
Two stages will be raced on Tuesday, the first over 69.7km from Dordrecht back to Rotterdam across the Dutch flatlands, followed by a 6.3 km individual time trial.
The race finishes on Sunday at Alpe d'Huez, a ski resort in southeastern France.
