Tries in either half by Andrew Bishop and Alun Wyn Jones laid the foundations for the victory sealed by the ten-point tally from inspirational fly half James Hook.
Jones said: "This is a breakthrough result for us. I sat here 12 months ago and it was a difficult time but we knew where we were. It was a horrible experience but we knew this year what was in front of us. It's part of growing up. We've won the Magners League twice before but we're absolutely delighted to win the cup.
"We had a dip last weekend but that's professional sport. We got a kick in the pants but we came back and knew what to do. There was a positive attitude and we performed admirably today.
"It was a comprehensive performance from 1-15. You keep improving and one day you will cross the line. We came here determined we would win."