Tim David earlier bludgeoned a spectacular 38-ball 74, and Marcus Stoinis chipped in with a 64 as Australia posted 186-6 in their 20 overs, and it was always going to require a disciplined bowling effort to deny India's batsmen.
Nathan Ellis bowled well for his three for 36, but Josh Hazlewood was sorely missed after he left the squad to prepare for the Ashes in the wake of his Man of the Match performance in the Melbourne victory on Friday.
Hobart-based seamer Ellis removed Abhishek Sharma (25) and Axar Patel (17) with bouncers and also trapped the other opener, Shubman Gill, in front for 15, but India never really looked under any pressure in the chase.
Sundar hit the first of his four sixes from the second ball he faced and enjoyed a stand of 35 with Tilak Varma (29) for the fifth wicket before Jitesh Sharma (22 not out) helped him to get India across the line in a partnership of 34.
India, who had the rare experience of winning the toss and choosing to bowl first, made three changes to their team from their loss in Melbourne on Friday, with returns for Sundar, Jitesh, and Arshdeep Singh.
"I think it was really important to win the toss, I think it was 19 or 20 tosses in a row, so good to break that streak," said India skipper Suryakumar Yadav.
"I think it was a great performance from all the three guys (called in). There was a good contribution from everybody, with the ball, with the bat, and I'm very happy to be on the winning side."
Left-arm seamer Arshdeep made an immediate impact by dismissing Travis Head with the fourth ball of the match and Josh Inglis in his second over to put Australia firmly on the back foot.
David, relishing his return to the ground where he plays his domestic T20 cricket, quickly put the hosts back in the ascendant with an astonishing barrage of boundaries to bring up his ninth half-century off 23 balls.
Spinner Varun Chakravarthy hit back for India by removing Mitch Marsh and Mitchell Owen from the other end with consecutive deliveries, but David continued to play his shots as Stoinis joined the party.
David had pummelled eight fours and five sixes when his luck finally ran out, and a brilliant catch on the boundary from Tilak off the bowling of Shivam Dube ended his innings and reduced Australia to 118-5.
Stoinis did not quite match the muscular power of David but put on 64 for the sixth wicket with Matthew Short (26 not out) before holing out at long on in the final over to give Arshdeep (3-35) his third wicket.
"We probably thought we were 20 (runs) short when we came off, but to India's credit, they bowled really well," said Australia captain Marsh.
"We had a good crack, but they were too good tonight."
The fourth T20 takes place on Thursday on the Gold Coast.
