A third successive defeat looked likely for the Heat who, chasing 124, slumped to 4-41 early and still required 29 off the last three overs.
But teenage New Zealand prodigy Amelia Kerr turned the game on its head, crunching seamer Belinda Vakarewa for 19 in the 18th over, including four boundaries, before securing victory by hoicking Vakarewa over mid-wicket with one ball remaining.
Kerr's late burst eased the pressure on gun opener Beth Mooney (44 not out), who shook off a blow to her left forearm from a Tayla Vlaeminck thunderbolt to hold things together for the reigning champions.
Earlier, left-arm orthodox tweaker Jess Jonassen snared three wickets in one over and finished with figures of 4-20 after Sammy-Jo Johnson (2-16) had wreaked havoc with the new ball as the Heat restricted the 'Canes to 8-123.
England captain Heather Knight (61 not out) stood out for the visitors and, while she had some support from prized recruit Nicola Carey (20), a Jonassen-inspired 4-7 collapse rocked the Hurricanes.
Next weekend the WBBL Heat team will head regionally to Mackay for the third season in a row for two matches against the Adelaide Strikers.