Ten Doeshate hit an unbeaten 68-ball 70 and added 103 for an unbroken third wicket stand with Bas Zuiderent (43no) as the Netherlands achieve the 137-run target with more than half of their overs left with consummate ease at Warner Park.
Earlier, Stelling grabbed 3-12 off eight economical overs as the Scots were bundled out for 136 in 34.1 overs.
Ten Doeschate hit off-spinner Majid Haq for three consecutive boundaries for the winning runs to loud applause from some 1,000 Dutch fans who had come to see their team's last match in cricket's showpiece tournament.
The win was the Netherlands' second in three World Cups after they beat Namibia in 2003, while the Scots finished win-less in their second Cup appearance.
John Blain had given the Scots a good start by dismissing Darron Reekers (nine) and Eric Szwarczynski (12) by the sixth over but ten Doeschate and Zuiderent were clinical and avoided any more losses.
Doeschate hit 13 boundaries and a six during his knock.
Earlier, Stelling dismissed Navdeep Poonia with the second ball of the innings before accounting for Gavin Hamilton (four) and Dougie Brown off successive deliveries in his fourth to rout the Scotland.
Stelling missed the Netherlands' second match against South Africa last week but came into his own right from the start to laid foundation for his team's win.
Tail-ender Glenn Rogers top-scored for Scotland with 26 which included five boundaries.
Neil McCallum (24) and Colin Smith (19) gave their team's total some respectability by adding 38 runs for the sixth wicket after they were reeling at 39-5.
Ryan Watson (16) John Blain (18 not out) and Colin Smith (19) also made double figures. The Netherlands bowled accurately after their stand-in captain Jeroen Smits won the toss and elected to field.
The Netherlands regular captain Luuk van Troost dropped himself on lack of form after his team went down to Australia and South Africa, the two top-ranked sides in the world, by 229 and 221 runs respectively.
South Africa and Australia, who have already qualified for the next round of Super Eight from the group, meet each other in a high-profile match here on Saturday.