Caunce saved two penalties for the Reserves Division One title winners as they saw off Wyre Villa at Blackpool Wren Rovers.
Goals from Craig Rowlands and Nick Buckley in either half did the damage to help Dylan Southern's men left the trophy.
Caunce sprung into action in the 17th minute, blocking Jonny Wilding's penalty before Rowlands put Euxton ahead on 29 minutes.
Caunce was called into action again in the 70th minute, once again denying Wyre Villa from 12 yards.
And Buckley made them pay with a killer goal from the edge of the box with 19 minutes left.
Wyre Villa will play in Reserve Division One next year after winning promotion this season.
Thanks to all at Blackpool Wren Rovers for hosting the final.
Keep up-to-date with our exclusive email newsletters.
Subscribe