Perry finished 68 not out from 46 balls, having shared a brilliant third-wicket stand of 86 with Alice Capsey (51 off 29), before hitting Heather Graham for 10 in two balls at the death to get Phoenix home.
Earlier in the piece, a powerful knock of 78 from 55 balls by Georgia Voll was the mainstay of the Fire’s innings and set Birmingham Phoenix a target of 145.
After a slow start in the powerplay that saw her and Ella McCaughan take the score to a run-a-ball 25-0, Voll put her foot down. She first stepped things up against the spin of Alana King and Linsey Smith, before she brought up her half-century with a maximum off Eva Gray.
Voll hit nine fours and two sixes in all, falling caught at long-on by Capsey off Smith from the 91st ball of the innings.
Sophie Devine then took over and ended things with a flourish. The powerful Kiwi cleared the ropes twice in the last six balls, off Smith and then King, to finish 35 not out from 18 balls and propelled the visitors to a total of 144-3.
Phoenix, watched on by part-owner Jude Bellingham, were seeking a first victory of the campaign but their pursuit didn't enjoy the best start - losing Davina Perrin fourth ball as she carved Potts to Georgia Wareham at point.
Tammy Beaumont and Capsey took the score to 33-1 after the powerplay but Phoenix lost Beaumont soon after when she holed out to deep midwicket off Wareham’s leg-spin.
Capsey was joined by skipper Perry and took the attack back to the Fire bowlers. They brought up their 50 partnership from 30 balls and then began to free their arms as they motored towards their target.
The game looked like it was in the hosts' hands, but with a record chase in sight - and Phoenix's first in 14 attempts - Capsey fell with 24 still required and the nerves began to jangle. Annerie Dercksen joined Perry and absorbed some early pressure before she handed over to the Australian legend to hit two late boundaries to earn Phoenix a much-deserved first win.
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