Stoinis, who turned up for Kings XI Punjab during the last IPL season, hit four boundaries and five sixes in a display of power-hitting to guide the visiting side to a formidable score.
Earlier, David Warner (64), skipper Steve Smith (55) and Travis Head (65) got some good batting practice ahead of the first ODI which would be played on September 17,
For the Board President's XI, all-rounder M S Washington Sundar was the best bowler, taking two wickets and giving away just 23 runs while medium-pacer Kushang Patel also got two scalps.
Brief scores:
Australia XI: 347/7 in 50 overs (Marcus Stoinis 76, David Warner 64, Steve Smith 55, Travis Head 65, Matthew Wade 45, M S Washington Sundar 2 for 23).