Hancock claimed 3-23 and Adelaide opener Laura Wolvaardt top-scored with 39 from 33 balls in Saturday night's final at Adelaide Oval.
Strikers captain Tahlia McGrath struck 38 from 34 balls and featured in a partnership of 66 with Wolvaardt.
The pair's second-wicket stand was the highest of the innings for the hosts, who are seeking consecutive WWBL titles.
Heat captain Jess Jonassen (1-19) and Georgia Voll (1-19) also took wickets for the visitors, who will become the WBBL's most successful franchise if they win a third title.
Adelaide won the toss but lost opener Katie Mack (three) in the second over - she chopped an attempted cut shot on to her stumps from Hancock's bowling.
Adelaide's Laura Wolvaardt plays a pull shot against Brisbane in the WBBL final. (Matt Turner/AAP PHOTOS)
McGrath and Wolvaardt then produced their brisk stand with the Strikers skipper the dominant force, hitting six fours and one six.
But McGrath's knock ended when she tried an expansive off-drive but missed and was bowled by Hancock.
Her dismissal left her side 2-71 after 10 overs - and Adelaide could muster only 54 runs from the last 10 overs.
South African Wolvaardt fell in the 15th over when stumped from a Jonassen spinner.
Her dismissal triggered a Strikers slide of 3-13 in an 18-ball span.
Bridget Patterson (11 from 17) and Madeline Penna (nine from 12) were dismissed in quick succession as Adelaide failed to gain any late traction.
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