With Mitchell Starc, Josh Hazlewood and Pat Cummins rested after the Test series, Richardson took figures of 4-26 from his 10 overs at the SCG, the best return of his young global career.
The hosts took a 1-0 lead in the three-match series on Saturday, winning the first ODI by 34 runs.
Desperate to shore up a World Cup defence that looked in bad shape after three wins from Australia's past 21 completed ODIs, the selectors made six changes.
"Justin has said it is a great opportunity to be able to push your selection [case] for the World Cup", he said. It got to a stage that if we didn't get a breakthrough, the game would have turned pretty quickly. So I think it'll be for me to concentrate on these two games coming up then if I'm lucky enough to get picked for the next tour, it'll be concentrating on those games.
Usman Khawaja scored 59 during his first ODI in nearly two years while Peter Handscomb, playing his first ODI in 15 months, top-scored with 73 after Aaron Finch opted to bat.
India's reply started badly when they slipped to 4-3, but Rohit's knock gave them some hope of victory.
He put on 137 for the fourth wicket with MS Dhoni (51), who became only the fifth Indian batsman to pass 10,000 one-day global runs during the course of his innings.
"While batting at No 5, in all these matches when I was going into bat, we required 150 to 160 runs and it was very important that I paced the innings well and played the role of a finisher", he added. It has been a tough road for last three years for me, but I am really focussed on white ball cricket. In Ranji Trophy also, I had bowled a lot this season.
"But [I am] more happy to get the win". There was a period there when they had a partnership through the middle and it nearly could have taken the game away from us. But we were lucky to get Dhoni out lbw and we kept getting wickets from there on.
"I just wanted to make sure we get those runs and the team gets into a good position". Peter Siddle saw through the middle overs and I thought all the bowlers bowled really well.