Chasing 275, India A were in a spot of bother after losing their top-order for a mere 51 runs and then reeling at 182 for six but Dhawan and Patel combined for a match-winning 93-run stand for the unbeaten seventh wicket.
Dhawan scored 56 off 55 balls while Patel hit 45 off 38 balls as India A chased the target with just eight balls to spare.
Before that stand, Kedar Jadhav (78 off 73) and Manoj Tiwary (50 off 75) had kept the Indian team in the hunt with their fighting half-centuries before being scalped by Ben Cutting (3/46).
White and his opening partner Phillip Hughes (51) had rattled up a 146-run stand to provide the hosts a solid start after deciding to bat.
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Once Huges was dismissed by Dhawal Kulkarni (3/51), India kept getting wickets at regular intervals and that helped them restrict Australia to a gettable total.
Alex Doolan (24) in the top and Ben Cutting in the lower order batted well for the hosts.
Brief Scores:
Australia A: 274 for 5 in 50 overs.(C White 137, P Huges 51, B Cuttign 35; D Kulkarni 3/51).