Afghanistan climbed to fifth in the standings with eight points, behind New Zealand on net run rate. The top four teams move into the last four.
Afghanistan had won only one game in two previous World Cups, but the Asian side now have four wins in the tournament in India having also beaten defending champions England, Pakistan and Sri Lanka.
"Of course we are 100% trying our best to make the semi-finals. If that happens that will be a big achievement for our country," Afghanistan skipper Hashmatullah Shahidi said after leading the run-chase with an unbeaten fifty.
"I lost my mother three months ago, so my family is in pain. That would be a big achievement, first of all to our country and then to my family also.
"Right now a lot of refugees are struggling. We are with them in this tough time, I dedicate this win to refugees who are in pain."
Chasing 180 for victory after the Netherlands won the toss and opted to bat first, Afghanistan were 55-2 but Rahmat Shah scored a breezy 52 off 54 balls to set the platform for a comfortable chase.
Skipper Hashmatullah Shahidi made an unbeaten 56 to guide Afghanistan home in the 32nd over, smashing the winning runs with his sixth boundary.
Earlier, Mujeeb Ur Rahman struck in the first over when he trapped opener Wesley Barresi lbw to claim his 100th ODI wicket and the next four Dutch batters were all run out after mix-ups.
Max O'Dowd looked set for a big score with nine fours but was run out by fine work in the deep from Azmatullah Omarzai, who shattered the stumps with a direct hit as the opener's dive was in vain.
Captain Scott Edwards - top scorer for the Dutch at the tournament - was run out first ball by Afghan keeper Ikram Alikhil when he played a shot and stepped out of the crease not knowing where the ball was.
"Definitely not ideal, four run outs in our top five is hard to come back from. I thought we started well and set ourselves up for a big total but gave it away," Edwards said.
"(We thought) 280 would have been a good score. We've done well batting first, we've been good defending scores."
Sybrand Engelbrecht was the lone middle order batter to provide resistance with a patient 58 but the Dutch were all out for 179 in the 47th over, with Alikhil involved in six dismissals and Mohammad Nabi picked up three wickets.
Afghanistan next play Australia and South Africa. The Netherlands, who are eighth, play England and hosts India.
