He dominated the opening stand of 59 with Unmukt Chand, in India A's chase of 227.
Leg-spinner Karn Sharma was the pick of India A's bowlers, with three for 37 in his ten overs.
The Australia A captain scored his third 50-plus score in the tri-series.
Burns was out for 41 in the 14th over, after helping build a base for a decent first innings total for the visitors.
Catch live updates from the final of the A-team tri-series, between India A and Australia A, here.
Australia A are still unbeaten in the tri-series and will be looking to sign off with a win.
India have made the final owing to massive wins over South Africa A.
Australia A chased the 259-run target set by India A with three wickets and 9 balls remaining.
Manish Pandey today said that lack of "better planning" and decent outing with ball hampered.
This is India A's second loss in three games in the tournament.