But Northern Ireland started brighter and Rock missed two attempts at a double which would have put them 4-1 ahead, before Clayton checked out on 142 to level the match at 3-3.
The Welsh duo pushed ahead to lead 7-5 but their opponents rallied to win the next four legs with a combination of Rock's scoring power and Gurney's finishing.
However, they missed four attempts to clinch the trophy and Wales levelled at 9-9.
But the Irish pair regrouped and Gurney finally nailed double eight for victory and settle a thrilling encounter.
Wales had fought back against the Dutch pair Danny Noppert and Gian van Veen to win 8-5 in their semi-final.
After four titles in the first eight editions of the tournament, the Netherlands had high hopes of a first triumph since Michael van Gerwen and Raymond van Barneveld's 2018 success.
The Dutch opened up a 4-2 lead on Wales before being pegged back at 5-5 after missed doubles from Noppert and it proved a turning point, with Price sealing victory in style by hitting double 20 twice.
Northern Ireland reached the final with a 8-1 demolition of hosts Germany, who had posted a shock last-16 victory on Saturday over pre-tournament favourites England.
Gurney averaged 105 as Martin Schindler and Ricardo Pietreczko were overcome.