Lee shared a 77-run partnership with Nat Sciver-Brunt (35 to 27) to iron out the majority of the chase.
Earlier, Perth won the bat flip and opted to bat but struggled to get their innings going, despite Hobart missing chances in the field.
In-form opener Beth Mooney (33 from 26) was dropped three times in the powerplay before being bowled by Heather Graham in the 11th over.
Graham (2-26) also picked up the big scalp of Scorchers’ skipper Sophie Devine.
New Zealand international Devine, who was dropped on 27, was circumspect early but came to life with two sixes, before getting stumped in the 17th over.
Hobart’s English spinner Linsey Smith bowled just two overs but finished with a valuable 2-4.
The Hurricanes earned a direct passage to the final after ending the season atop the table, while Perth, who were gunning for their second title, won two finals games to qualify.
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