Van Beek struck 30 with the bat before taking the ball and conceding just eight, leading his side to a victory which saw them finish second in Group A and take two valuable points into the Super Six stage.
A Harare thriller saw both sides finish on 374 from their 50 overs, at which point van Beek took centre stage.
Having fallen falling to the final ball of the regular innings for a 14-ball 28 with just a single required, the all-rounder struck three sixes and three fours from the super over bowled by Jason Holder.
Holder had earlier held a brilliant catch to dismiss van Beek and force the unlikely tie but the Dutchman then seized control, removing Johnson Charles and Romario Shepherd with consecutive balls following his fireworks with the bat to decide the outcome.
The Windies started strongly with the bat after being put in as openers Johnson Charles and Brandon King (76) added 101 before the former was trapped lbw for 54.
Saqib Zulfiqar dismissed Sharmah Brooks (25) and King (76) in consecutive overs before another century stand, this time between Shai Hope and Nicholas Pooran, ended when Hope was caught on the rope looking to bring up a half-century with a maximum.
Pooran brought up his second consecutive century before kicking on with Keemo Paul as the Windies hammered 61 off the last five overs.
Netherlands openers Vikramjit Singh (37) and Max O’Dowd (36) added 71 inside 10 overs in reply but Roston Chase dismissed both as West Indies fought back.
Wesley Barresi (27) and Bas de Leede (33) kept Netherlands on track and after both were removed by Akeal Hosein, Teja Nidamanuru and captain Scott Edwards put on 143 from just 15 overs to set up a frantic finish.
Edwards (67) was first to go and the game was back in the balance when centurion Nidamanuru (111) picked out Chase at third man.
Aryan Dutt (16) and van Beek took the equation to five from as many balls but Joseph took two wickets at the death to force a super over.
Van Beek made no mistake at the second time of asking to lead his side to a momentous victory following their highest-ever ODI score.
