Josh Rock and Daryl Gurney were reduced to tears after pipping two-time winners Gerwyn Price and Jonny Clayton 10-9 in Sunday's final.
They had a back-and-forth match in their hands but allowed Wales to force a decider, which saw Northern Ireland reset to become champions for the first time.
"We've made history for Northern Ireland and we're so proud as a team," Rock said afterwards.
"As a team, we were fantastic and we fought hard all the way through."
Northern Ireland, who began the day with earlier wins over the Republic of Ireland and Germany, started well by opening a 3-1 lead.
That came before Wales rallied back to lead 7-5, which caused a Rock-inspired Northern Ireland to show some scoring power.
But they squandered four opportunities had an opportunity to seal the title, allowing Wales to level at 9-9 and make it a one-leg shoot-out.
Rock and Gurney, though, held their nerve with the latter pinning double eight to trigger emotional celebrations.
"I would like to congratulate Wales, it shows the class of the Welsh team to stay on stage and congratulate us," Gurney said.
"Jonny and Gezzy are legends of the game. I think they'll go on and win big titles this year."
"We started off really slow, trying to get in the game was really difficult," Wales' defeated Price admitted.
"Testament to the Northern Irish team, Josh's scoring was unbelievable and we couldn't keep up with them.
"At 9-9 we gave ourselves a chance but they were a bit better than us and they deserve it."
Northern Ireland had earlier fought back against Ireland to win 8-5 before demolishing hosts Germany 8-1 to reach the final.
Wales, meanwhile, moved past Hong Kong 8-4 and produced a fightback of their own by beating the Netherlands 8-5.