The 27-year-old former World Matchplay winner took full advantage of a nightmare start from two-time world champion Anderson when racing into a 8-0 lead.
'The Flying Scotsman' averted his fears of a whitewash when halving the deficit but left himself with a mountain to climb.
Two-time World Youth champion Van den Bergh edged closer to victory at 10-4 but missed three match darts in leg 15 - but the 27-year-old shut the door on an Anderson comeback when following up with a fourth 180 in a 14-darter to pocket the £20,000 top prize in Copenhagen.
"I have dreams. I am chasing my dreams, and winning against a player like Gary - that is going to help me," said Van den Bergh.
"You know that Gary isn't going to give it to you, you have to work for it, that's what I had to do, and I managed to make myself a champion, against a player who is a champion."
The Belgian thrower added: "The sky is the limit. Just look at the trophy I'm holding in my hands. I've dreamed about it, I've managed to make my dreams come true."
Van den Bergh opened Saturday's finals day with a 10-5 win over Gerwyn Price before scuppering in-form Michael Smith's hopes of successive World Series titles with an 11-4 success in the semi-finals.
Anderson beat Peter Wright 10-4 in the quarter-finals and James Wade 11-7 in the last four.
The World Series of Darts continues with the inaugural Dutch Darts Masters at the Ziggo Dome in Amsterdam from June 24-25.