Sutherland was dropped on 12 and 24 on her way to an impressive 110 off 95 balls as Australia posted a daunting 6-298 in 40-degree heat on Wednesday.
In reply, India were bowled out for 215 in 45.1 overs as Ashleigh Gardner claimed a career-best 5-30 in front of 1484 fans.
Smriti Mandhana (105 off 109 balls) played a lone hand for India with the bat amid a sloppy fielding display from Australia.
Mandhana was dropped on 27, and Harleen Deol (39) received lives on 21 and 33 as India moved to 3-189 in the 36th over.
But when Gardner bowled Mandhana, it triggered a collapse to 6-14 as India's victory hopes imploded in a flash.
Australia dropped five catches during India's innings - an effort they will be aiming to fix ahead of their three-match ODI tour of NZ and the home Ashes series in January.
Annabel Sutherland bringing up a ton at the WACA, it's just meant to be!— 7Cricket (@7Cricket) What a knock for her second ODI 💯 #AUSvIND pic.twitter.com/Q2E7s6TmQGDecember 11, 2024
Georgia Voll limped off late in India's innings after a fielding mishap in which she appeared to hyper-extend her knee, but it didn't look serious.
Although Australia were butter-fingered in the field and they suffered a top-order collapse, Sutherland's second ODI century and handy scores from Gardner (50 off 64 balls) and Tahlia McGrath (56no off 50 balls) ensured the hosts had an easy win.
It marked Sutherland's second century at the WACA Ground this year, following on from her 210 in Australia's Test win against South Africa in February.
"She's one of those players that's probably the last (to leave) at every training session, so it's no surprise she's able to do that in those tough conditions," Gardner said of Sutherland's heroics in the heat.
"And we've seen it before, when we played the Test match here, she made 200 and that was 35-plus (degrees) as well.
"I think she just really relishes in the environment when there's a little bit of pressure on for the team.
"She's a serious player, but it's pretty scary how good she's going to get in the future."
But it was far from smooth sailing for the hosts.
Australia slumped to 4-78 in the 17th over on the back of a stunning spell from fifth-gamer Arundhati Reddy (4-26 from 10 overs).
Annabel Sutherland cracked 110 off 95 deliveries after Australia were in a spot of bother. (Richard Wainwright/AAP PHOTOS)
It should have been 5-82 - only for Gardner to receive lives on consecutive deliveries when she was on just three.
Gardner was dropped by Jemimah Rodrigues, and then one ball later given out LBW - only to have the decision reversed on review.
That robbed Reddy of what would have been her maiden five-wicket haul.
Gardner went on to make her sixth half-century, while Sutherland did even better in a knock that featured nine fours and four sixes.
Reddy was not selected for the first two games of the series, but the 27-year-old Indian was a destructive force at the WACA.
Openers Phoebe Litchfield (25 off 33 balls) and Voll (26 off 30) guided Australia to 0-58 from 10 overs after the hosts lost the toss and were sent in to bat in the stifling Perth heat.
But Reddy's introduction sparked a collapse of 4-20, with the Indian pace bowler claiming all four wickets.
Arundhati Reddy rocked Australia's top-order with figures of 4-26 off 10 overs. (Richard Wainwright/AAP PHOTOS)
Reddy's first wicket on Australian soil was a memorable one, with the ball swinging in beautifully to clean bowl Voll.
Litchfield fell three balls later when she edged one behind, and Perry's bid to post back-to-back centuries ended early when she was bowled by Reddy for four.
Beth Mooney was sent packing for 10 when she edged Reddy behind, but India's sloppy fielding cost them dearly as both Sutherland and Gardner were let off the hook multiple times on the way to their big scores.
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