A revised victory target of 317 in 33 overs following a rain interruption left Australia facing a daunting task and they ran out of steam after David Warner's departure for a defiant half-century, as India prevailed via the Duckworth-Lewis method.
Spinner Ravichandran Ashwin, playing in only his second ODI this year, got rid of Australia's dangerous batsmen to end with 3-41 after pace bowler Prasidh Krishna's early double strike.
Asked to bat first on a good Holkar Stadium wicket by stand-in Australia captain Steve Smith, top-ranked India posted a huge 399-5 in 50 overs as opener Gill continued his superb form with a fifth ton this year and sixth overall.
The 24-year-old began cautiously but built momentum to make 104 off 97 balls, with six fours and four sixes, while Iyer gave him good company with 105 from 90 balls as the pair tore into the Australian attack without rested skipper Pat Cummins.
Iyer's third century in the format will be a huge confidence boost after the 28-year-old missed the Indian Premier League and the World Test Championship final earlier this year with a lower back injury that required surgery.
He also missed much of India's triumphant Asia Cup campaign with a back spasm but showed he was in fine fettle heading into the World Cup on home soil next month, with 11 fours and three sixes in a controlled 200-run second-wicket stand with Gill.
Home skipper KL Rahul made a steady 52 in the middle overs before Suryakumar Yadav heaped the misery on Australia, striking four consecutive sixes off Cameron Green in the 44th over en route to a 37-ball 72.
Australia started shakily as Krishna removed Matthew Short and Smith off successive balls before rain briefly halted play with the tourists mounting a fightback at 56-2.
Left-hander Warner went on the offensive after play resumed and displayed his ambidexterity by batting right-handed against Ashwin, but was trapped lbw for 53 as he looked to switch back and raise the scoring rate.
Warner bizarrely did not review the umpire's decision as television replays showed he edged the ball onto his pad.
Ravindra Jadeja (3-42) then got in on the act as Australia fizzled out for 217 after a battling 54 by Sean Abbott.
India, who rested several frontline players for the first two games, will eye a clean sweep when the teams meet in Rajkot on Wednesday. They begin their World Cup campaign on October 8th against Australiac.
