The defending champions struggled in the opening stages when Australian Georgia Redmayne was dismissed early without scoring and Emily Arlott bowled both Cordelia Griffith and Charli Knott.
Kira Chathli underpinned the innings with a fantastic 69 runs from 35 balls, but her effort was ended after edging Perry, the Phoenix's Australian captain, behind.
Another Australian, Grace Harris, picked up where Chathli left off with a quickfire 34 before being trapped lbw by Arlott for her third wicket as the Spirit closed on 6-164.
Aussie opener Georgia Voll fell early for eight in the Phoenix's chase and Emma Lamb enjoyed a bright start before being run out for 23, the highest score of their innings. Perry departed after adding five.
Amy Jones and Arlott both finished with 10 runs and were the only other players to make double figures.
Meanwhile Manchester Originals edged to a five-run win against the Northern Superchargers.
England bowler Kate Cross removed Kathryn Bryce and Australian Beth Mooney early on but Deandra Dottin hit a brilliant unbeaten 51 from 26 deliveries to help the Originals post 5-117.
Bryce found an early breakthrough when Davina Perrin hit her delivery to Sophie Ecclestone, but the Superchargers gained control with Alice Davidson-Richards and Australian Phoebe Litchfield's partnership.
The pair blasted 64 runs from 47 balls before Litchfield was dismissed for 31 by Bryce for her second wicket and Kerr soon took the scalp of Davidson-Richards, who fell for 29.
Wickets suddenly fell in quick succession as another Superchargers Aussie, Annabel Sutherland, was caught by Fi Morris off Ecclestone and skipper Hollie Armitage was bowled by Kerr.
And some solid bowling at the death saw Ecclestone take Bess Heath's wicket and Bryce caught Cross off Lauren Filer for the Originals to narrowly claim their third win of the competition.
