Claremont-Nedlands bowler Kelly was 12th man in the 19-run win over New Zealand on Sunday but came in to the side to face India at the expense of Alex Gregory who suffered a minor injury.
And Kelly made the most of his opportunity, taking 2-45 from 10 overs as Australia bowled India all out for 221 inside 50 overs. Kelly took the vital wicket of opener Ankush Bains for 64 and Sarfaraz Khan to suddenly have India 4-180.
However in reply Australia was unable to chase down the target, with the Indian attack impressing.
South Perth batsman Leaver, who made 31 in Sunday's win over New Zealand, opened the batting but was dismissed for 1 off 6 deliveries bowled by opening paceman Abhimanyu Lamba.
Kelly arrived at the crease batting at number seven, managing only 4 runs off 10 balls before being caught by Shreyas Iyer off Deepak Hooda as Australia lost 6-19 to be 174 all out.
Australia's next game is a warm-up clash against Papua New Guinea on Thursday.