Opening the batting, Piparo guided the Swans to their first A-Grade 50-over flag since 2010 with a match-winning knock of 115 not out from 136 balls.
The triumph ended Melville’s dominance in recent years, but it was not easy, with the Swans slipping to 6-197 and 8-225 in pursuit of the Storm’s 5-244.
Swans skipper Piparo got her side home with 11 balls to spare, with solid support at the death from Caitlin Couch (10) and Hannah Merritt (4no) under pressure.
Earlier, Storm captain Renee Chappell won the toss and elected to bat, with Melville losing the experienced Jenny Wallace to an early run-out for 10.
Rebecca West (41) and Mathilda Carmichael (67) got Melville back on track, to be 2-181.
Emma Biss (51 from 46) crunched five fours and a six in her quickfire half-century, while Chappell chipped in with 28 as Melville reached a strong score.
Rachel Baines was Midland-Guildford’s best with the ball with 2-49.
In reply, the Swans lost Taneale Peschel second ball lbw to Biss, but rallied through Piparo and Bhavisha Devchand.
The pair put on 125 for the second wicket, before Fury batswoman Devchand was caught by Wallace off Chappell for 62.
The Swans struggled for partnerships from then on, but Piparo was the constant as wickets fell around her.
Emily Bowden and Couch were both run out as the pressure begun to build, while Chappell (2-53) and Carmichael (2-40) both claimed two wickets with the ball.