The teammates overcame Austria's Mensur Suljovic and Rowby-John Rodriguez 3-1 in Sunday's final after four days of competition at the Sparkassen-Arena in Jena.
Wright and John Henderson eased through their first round opener on Thursday, whitewashing China 5-0 to set up a quarter-final meeting with Poland.
A 2-0 victory saw the duo progress to Sunday’s finals day and a quarter-final against Netherlands, where Michael van Gerwen and Dirk van Duijvenbode were defeated 4-1.
The Scots then knocked out defending champions Wales in the semi-final with Henderson defeating world number one Gerwyn Price 4-2 in his singles match before Jonny Clayton beat Wright 4-2 to take the match to a pairs decider, which Wright and Henderson won 4-3 to advance to the final.
In the final they faced an Austria pair hoping to become the first unseeded nation to win the tournament.
After splitting the two singles matches, with Suljovic beating Henderson and Wright beating Rodriguez, the match progressed to the pairs, where Henderson threw a winning double in the deciding leg to keep Scotland alive.
Victory was secured in the next singles match as Wright missed five darts for the title before eventually overcoming Rodriguez to clinch a second World Cup title in three years for Scotland, following Wright and Gary Anderson’s 2019 success.
A first PDC title for Henderson, who was a late replacement for Anderson and was in tears at the end, means Scotland are just the second nation to win with a different pairing since the tournament’s inception in 2011.