Wright - who earlier defeated world champion Michael Smith in the semi-finals - got off to a flying start, taking out three ton-plus finishes, including a 140 checkout, as he opened up a commanding lead 5-0 at the first session interval.
Price, runner-up at last weekend's Bahrain Darts Masters, recovered from 8-2 down to trail 9-5 with a fine 156 finish.
Wright, though, went on to take the next two legs and wrap up an impressive victory with an average over 102 for his first TV title since landing the 2022 World Championship.
Earlier in Saturday's semi-finals, which opened the evening session at the Forum Copenhagen, Wright had ended Smith's 12-match unbeaten run with an 11-8 success.
'Snakebite' saw Smith - chasing a third successive TV title after victory in Bahrain - fight back from 5-1 down to level, but the Scottish two-time world champion recovered to close out victory, landing 50 per cent of his attempts at a double.
Price, meanwhile, pulled off a dramatic 11-10 win over his Wales World Cup partner Jonny Clayton with a 101 average and hitting 11 maximums.
On Friday, all eight of the PDC contenders had made it through against regional players in the first round of the World Series event in Denmark.
In the quarter-finals on Saturday afternoon, Wright edged out World Championship runner-up Michael Van Gerwen on a final-leg decider while defending champion Dimitri Van Den Bergh was beaten 10-7 by Price.
Clayton dispatched third seed Rob Cross 10-4 and Smith held off a fightback from Luke Humphries to progress with a 10-7 victory during which he landed eight maximums.