Australia claimed a series victory, taking a 2-0 lead in the best-of-three series, with Thursday night's triumph at Adelaide Oval.
India posted 9-264, with Rohit Sharma (73 from 97 balls) top-scoring and Australia's Adam Zampa (4-60 from 10 overs) and Xavier Bartlett (3-39 from 10) the chief wicket-takers.
In reply, Australia reached 8-265 from 46.2 overs, with Short making 74 from 78 balls, Connolly an unbeaten 61 from 53 in his fourth ODI innings, and Owen 36 from 23 in his first bat in an ODI.
The inexperienced duo of Connolly and Owen featured in a match-defining 59-run partnership that led Australia from danger.
Coming together at 5-187 in the 36th over, Connolly - who had made just 10 ODI runs before his Adelaide outing - struck five fours and one six, while Owen cracked three sixes and two fours.
"It was good fun," Connolly told the host broadcasters.
"My first couple of innings playing for Australia, I actually didn't bat, I was just sitting on the side watching the boys.
"But super-stoked for the boys to get the win.
"I was quite nervous walking out to bat, but I just took it all in and enjoyed it as much as I could."
Connolly reached his half-century from just 42 balls after Australia lost openers Mitch Marsh (11 from 24 balls) and Travis Head (28 from 40) inside 13 overs.
Short, batting after suffering a painful split on a finger on his right hand while fielding, and Matt Renshaw then steadied with a 54-run partnership.
But just as the duo appeared set to cash in, Renshaw (30 from 30 balls) was bowled, leaving Australia 3-109 in the 22nd over.
Alex Carey (nine) fell cheaply and was soon followed by Short, who also posted his highest ODI score, 74 from 78 balls.
Short's exit brought Connolly and Owen together, with the latter dismissed when the home side required just 17 Â runs to win.
Earlier, Indian legend Virat Kohli made consecutive ducks for the first time in his esteemed ODI career.
Kohli, who made his ODI debut in 2008, had never previously been dismissed without scoring in successive one-dayers.
But the former Indian captain followed his duck in the series-opener in Perth on Sunday with another in Adelaide.
In his 304th ODI, Kohli was trapped on the crease and struck on the pads in Bartlett's second over of the game.
Australia summoned Bartlett to the team, for his fifth ODI, with near-instant reward.
The Queenslander, with the first ball of his second over, removed Indian captain Shubman Gill (nine), then claimed the prized wicket of Kohli four balls later.
The Indians were 2-17 after seven overs before ex-skipper Sharma (seven fours, two sixes) and Shreyas Iyer (61 from 77 balls, seven fours) rallied with a 118-run partnership.
The series concludes in Sydney on Saturday, before the nations meet in five T20 matches starting next Wednesday.
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