Third-placed England suffered their first loss in the tournament as the defending champions chased down a target of 245 with 57 balls to spare, as Gardner scored 104 off 73 balls, hitting 16 boundaries, while Sutherland stayed unbeaten at 98 in their partnership of 180.
Both England and Australia have already qualified for the semi-finals along with South Africa, while India, New Zealand and Sri Lanka continue to battle over the last available spot.
"It was pretty fun, always good batting with Ash. She keeps the game moving, pretty good seat up the other end," said player of the match Sutherland, who also took three wickets after Australia put England to bat first.
England openers picked up 55 runs in the first eight overs with Tammy Beaumont scoring double digits in two of Kim Garth's overs, but Sutherland's (3-60) wicket-maiden in the ninth over sent back Amy Jones (18) and plugged the flow of runs.
England scored only 36 runs in the next 10 overs, with Heather Knight (20) being trapped lbw by Sophie Molineux (2-52) on Indore's spin-friendly track.
Captain Nat Sciver-Brunt (7) fell to Alana King, leading to a 12-over period where England's only boundary came from a misfield resulting in four byes. King allowed just 20 runs in 10 overs, and Beaumont's (78) resistance ended when she was caught trying to hit Sutherland for a six.
England were struggling at 168-6 after 40 overs when Charlie Dean (26) and Alice Capsey (38 off 32) tried to turn things around, adding a quick 61 runs in their seventh-wicket partnership that helped them reach 244-9.
Gardner leads the way
Australia got off to a shaky start, with openers Phoebe Litchfield (1) and injured skipper Alyssa Healy's replacement Georgia Voll (6) sent back early, and Ellyse Perry's leading edge flying back to bowler Linsey Smith, leaving them at 24-3 in the sixth over.
Beth Mooney (20) helped Sutherland stabilise the innings with a 44-run partnership for the fourth wicket, and once Gardner settled in, the pair added runs quickly.
England, who have played in three of the last four World Cup finals and won two, could not build any pressure on the batters as Gardner completed her fifty in 47 balls.
Sutherland remained steady on the other end as Gardner took just 22 more balls to complete her third century in the format and scored the winning runs with a lofted drive down long off.
England skipper Sciver-Brunt said her team did not have enough runs to defend.
"I don't think we've played our best game yet, so we'll be ready for (Australia) if we do see them again," she added.
Hosts India face New Zealand on Thursday.