Tigers won the NIHL National Cup after winning the tie 14-7 on aggregate.
Tigers led 6-4 from the first leg and scored three goals in the opening six minutes of the contest, Brandon Whistle (2) and Ricky Plant scoring. Peterborough pulled a goal back but Jason Silverthorn restored the three-goal advantage to make it 4-1.
Tigers added further goals in the second period through Ross Kennedy and Whistle, who completed his hat-trick. Peterborough scored again to make it 6-2 but Joe Aston netted a seventh for Tigers.
Scott McKenzie scored an eighth goal early in the third period.
Peterborough had the final say on the scoresheet late on but Tigers ended a dominant performance to win the cup and celebrate wildly at the final buzzer.
Delighted head coach Tom Watkins said: “We had a fantastic start and never looked back from there.
“We kept getting the puck deep and getting to the front of the net, all round it was a first-class job from the boys.
“We had a great crowd in and it was fantastic to see the place jumping.”
Tigers’ comfortable lead allowed Watkins to give minutes to some of his younger players.
“We’ve played four games in six days,” he added. “The only time we’ve struggled this year has been when we’ve lost bodies.
“We’ve had more injuries than most and some key players out the line-up. You need guys to step up.
“Our young guys have got to learn these situations and it was a great experience for them.”
Owner Mike Washburn added: “We have the best team, best coach, best support.
“You can invest cash, but at the end of the day these guys have pulled together and pulled the results out.
“On occasions it’s just about grit and determination and you can’t buy that. I’m really proud of the guys.”