Chasing 180 to win Giants found Mumbai's multi-national attack too hard to handle and lost by nine runs.
New Zealand leg-spinner Amelia Kerr took 3-34, West Indies' Hayley Matthews 3-38, including Beth Mooney for seven, and South African pacer Shabnim Ismail 2-17 in her four overs including Gardner for a duck and Phoebe Litchfield for 22.
Victory for Mumbai, or even a tie, in the final match of the group stage against last-placed Royal Challengers Bengaluru on Tuesday will put them in Saturday's final, pitching Giants against Meg Lanning's Delhi Capitals in Thursday's eliminator.
Gardner put Mumbai, playing at their Brabourne stadium home, in to bat after winning the toss and led by example. She took 1-27 off her four overs, Giants' best figures, dismissing the dangerous Englishwoman Nat Sciver-Brunt caught and bowled for a 31-ball 38.
Gardner also ran out Kerr (five) with a superb direct hit, and caught Amanjot Kaur (27 off 15) to limit a late flurry.
Harmanpreet Kaur top-scored for Mumbai with 54 off 33 before being caught in the deep by Litchfield.
Giants needed to knock off the runs in 18 overs to go top of the table and, said Gardner, approached the target with that uppermost, pushing the required rate to ten-an-hour. But wickets fell as they attempted to swing the bat and by the 11th over they were 5-70 and well behind the clock.
Bharti Fulmali, with a 25-ball 61, kept them in the match but in the end it was too much, Giants being all out off the last ball.
Gardner was left to hope that, if Giants meet Indians again, be it in the eliminator or the final, they would finally "change that tune".
