Van der Poel, whose father Adri won the one-day race in 1986, launched the two-man sprint and managed to just hold off Van Aert after 241 kilometres.
"It's incredible," van der Poel said about winning the Belgian Monument 34 years after his father. "Maybe number 51 (as my father) told me, now I'm starting to believe it."
"I was dead in the sprint, neither of us knew who had won. And I made a really good throw to the line and that made the difference.
"They had already called my name twice, I simply can't believe it.
"I asked 10 times for confirmation after I crossed the line if I had won or not. I have no words. I am speechless."
Alaphilippe, who had split the peloton with an attack in the Kopperberg, went head over heels after his right elbow clipped the back of a race motorbike 35km from the line after the trio had broken clear.
26-year-old van der Poel, riding just in front of the Frenchman, narrowly avoided the bike on the right side of the road.
Alaphilippe eventually sat up, holding his right arm and screaming in pain before being attended to by race doctors.
Deceuninck-QuickStep has since confirmed the world champion was taken to the hospital where X-rays showed fractures of metacarpal 2 and 4 on his right hand.
Van Aert had been looking to become the first rider to win the Tour of Flanders and Milan-Sanremo in the same year since Eddy Merckx in 1975.
"A few motorbikes wanted to go behind us, because our gap was growing, I wanted to take profit as much as possible to go behind the moto,' van Aert said.
"And I think Julian was not concentrating or something. It's a real pity that he hit the moto."