The two riders entered the final kilometre of the race with only each other for company, after Wout Van Aert (Jumbo-Visma) was dropped on the final ascent of the Oude Kwaremont.
Considered a far superior sprinter to Asgreen, Van der Poel was the clear favourite to cross the line first, but in a huge upset it was the Dane that turned on the speed to claim a famous victory.
A clearly disappointed Van der Poel showed respect to his opponent after the race, shaking hands with Asgreen and acknowledging he was a bit off the pace and beaten fair and square by a better rider on the day.
"I think I lost to a stronger guy today," Van der Poel said. "It says enough when he keeps riding with me until 1km from the finish line, that he is also sure about his own sprint, and I already felt during [the] race he was really strong today.
"For me, the legs were a bit off in the end, so I’m quite disappointed but I think I lost to a stronger guy today so that makes it easier to accept.
"I think did really good race but in the end, there was one guy stronger. I already noticed on the hills that he was one of the strongest guys. When I attacked it was always him who was fastest to follow."
Van der Poel was impressed by the attacking mentality of Asgreen, who many expected to approach the race very differently.
"Asgreen is certainly the deserved winner," Van der Poel said.
"He never made a point of riding to the finish together. That says enough.
"He felt good. I certainly didn't think it was a done deal. In the sprint I could turn it on for five seconds, then it was just off. He is someone who dares to race and dares to continue to the finish, I like that."