But India's appeals fell on deaf ears with Richard Kettleborough adjudging it not out.
And with India steadfastly refusing to allow the use of DRS in any games they're involved in, it meant Bailey was off the hook.
Hot Spot replays showed a faint brush of Bailey's gloves, while snicko registered a noise as the ball passed the gloves.
Bailey emphatically made the most of the reprieve to set up the series-opening win, crunching seven fours and two sixes in his match-winning knock.
Smith was even more brutal in posting his highest ODI score, eclipsing his previous best of 105.
But he was out in the last over when he chipped a catch to cover when just two more runs were needed for victory.
Sran finished with 3-56 in an impressive debut, and it would have been even better with the help of DRS.
Australia's debutant pacemen didn't fare so well.
Victorian Scott Boland was economical early.
But some full tosses at the death proved mightily costly, with the 26-year-old conceding 30 runs from his final two overs to finish with 0-74.
Paris showed promise but lacked the killer punch on the way to 0-53 off eight overs.
Josh Hazlewood led the bowling brilliantly in the absence of pace stars Mitchell Starc and James Pattinson.
After conceding 11 runs in a wobbly first over, the 25-year-old rebounded strongly to finish with 1-41 from his 10 overs.
Indian opener Rohit Sharma struck an unbeaten 171 from 163 balls to spearhead the visitors' 3-309.
Sharma combined with Virat Kohli (91 off 97) for a 207-run stand.
The partnership was India's highest-ever second-wicket stand against Australia, eclipsing the 199 set by Sachin Tendulkar and VVS Laxman in Indore in 2001.
Sharma's knock was also the highest score by a visiting batsman against Australia in Australia since Viv Richards' 153 not out for the West Indies at the MCG in 1979.
Australia all-rounder Mitch Marsh, who will be rested from the second one-dayer in an attempt to nurse his body through the series, grabbed at his troublesome hamstrings a few times throughout India's innings.
But he stayed out on the park to finish with 0-53 from his nine overs, before making an unbeaten 12 with the bat.
Bailey broke out into a grin when asked whether he had gotten any glove to the ball.
"It just caught the thigh guard a little bit I reckon," he said.
"It would have been interesting on DRS to have a look at that, wouldn't it."
India captain MS Dhoni hinted his team might be getting punished by umpires for the team's ongoing refusal to use the DRS.
"Are you indirectly saying that we don't get decisions in our favour because we don't use DRS," Dhoni replied when asked about whether he would consider changing his tune on the DRS.
"We need to push the umpires to take the right decision.
"You have to see how many 50-50 decisions doesn't go in our favour.
"But I'm still not convinced about DRS."
HIGHEST AUSTRALIAN PARTNERSHIPS IN ODI CRICKET
*260 - David Warner and Steve Smith v Afghanistan in Perth, 2015
*252* - Shane Watson and Ricky Ponting v England at Centurion, 2009
*246 - Aaron Finch and Shaun Marsh v Scotland in Edinburgh, 2013
*242 - George Bailey and Steve Smith v India in Perth, 2016
