Gardner, the Rockets' captain, ripped the heart out of the home innings, taking four wickets at the cost of 16 runs from 18 balls.
Despite the absence of England captain Nat Sciver-Brunt, the Rockets ran up 8-153 thanks to Sophia Dunkley's 57 off 33 balls, with Sophie Luff contributing 51 off 26 deliveries.
While another Australia star, Beth Mooney, was dismissed for just two, Dunkley and Luff, batting in Sciver-Brunt's usual position of No.3, put on 91 to anchor the innings.
Sophie Ecclestone collected a couple of wickets as the Rockets lost their way, with Gardner and fellow Aussie Kim Garth going cheaply, but a 154 target proved too much for the Super Giants, who were all out for 122 in 93 balls.
Gardner orchestrated the destruction while Dunkley also claimed three catches as Super Giants, previously unbeaten in three, slipped to a 31-run loss.
Meg Lanning made 35 off 24 balls before departing lbw to fellow Aussie Gardner, who also spectacularly caught and bowled Paige Scholfield.
Another Aussie bowler, Sam Bates, also caught and bowled Jo Gardner, then Gardner mopped up the final two wickets without conceding a run as the Super Giants were brought down to earth.
