Thirty-five-year-old Price, a former Rugby Union and Rugby League player, also became the new world No. 1 with his victory at Alexandra Palace in London.
Price had to hold his nerve in a thrilling contest against two-time champion Anderson.
The Welshman stormed into a 5-1 lead in their best-of-13 final and, although he faltered with the title in sight, Anderson failed to capitalise.
Price, who hit 13 180s compared to Anderson’s 10, appeared to be cruising to his first world crown, but he staggered over the finish line after missing 11 match darts in total.
In the penultimate set, Price failed to hit double 10 and double five to secure the triumph and seemed to have missed his chance as Anderson took the first two legs in the final set.
But Price still scored more heavily than his opponent and, when needing double five for victory in the deciding leg, he stepped away from the oche before finally hitting the winning target.
Former champions were quick to acknowledge Price’s achievement, with 14-time winner Phil Taylor writing on Twitter: “Congratulations to @Gezzyprice welcome to the Club pal you played brilliant.”
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