Her side chasing 148 for victory, veteran Elyse Villani helped the Hurricanes overcome some middle-order wobbles and take control at Bellerive Oval.
The hosts required 19 runs from the last three overs with four wickets in hand.
Aussie international Gardner (4-36) had been expensive, going at 1-34 across her first three overs, but was thrown the ball with Saturday's game hanging in the balance.
The Sixers skipper dispatched of Hayley Silver-Holmes (6) as she attempted an audacious sweep shot before also collecting Molly Strano's stumps as the tweaker attempted a hero shot of her own on the next delivery.
Lauren Smith (1) mistimed Gardner's last ball of the over and picked out Sophia Dunkley at extra cover, leaving Hobart with only No.11 Linsey Smith to partner Villani (42no).
When Smith skied to mid-wicket off Lauren Cheatle, the Hurricanes were all out on 136 and left to wonder how the game had slipped so quickly out of their hands.
The victory ends the Hurricanes' winning streak on five - their equal-longest in WBBL history - and helps the Sixers bounce back from a disastrous 111-run loss in a rain-affected last start against the Melbourne Stars.
Earlier, the summer's leading wicket-taker Heather Graham (4-29) came up with WBBL career-best figures to help consign the Sixers to 9-147 at the close of their innings.
That was no mean feat after the visitors won the toss and looked in command during a 75-run opening stand between Dunkley and Ellyse Perry.
Dunkley notched her second half-century of the summer after surviving a scare on seven, the third umpire ruling her bat came down in time to thwart Lizelle Lee's stumping effort.
But the Sixers' innings never hit the same heights after Dunkley (50 off 46 balls) lobbed Graham's slower ball out to Rachel Trenaman at long on.
Only Gardner (25) joined Perry (28) and Dunkley in passing 50 as the Sixers lost 4-6 to finish their innings with Graham on song.
Graham had her four-fer by collecting Erin Burns' stumps as the veteran stepped back and mistimed her shot.
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