Burns had been the subject of much speculation in the lead-up the First Test against India following poor recent form with the bat and he hardly helped his cause with a scratchy 8 in the first innings.
However, Burns was more impressive in the second innings, scoring 51no including a six for the winning runs, as Australia comfortably chased down the meagre target of 91 on day three of the day-night Test match.
“Burnsy is a really important part of our team and all cricketers know how hard it is when you’re going through a run like that,” Paine said.
“To come out in Test match cricket and try and find your way out of it it’s a very, very difficult place to be. It will do his confidence the world of good.”
Burns also underwent scans for a broken arm but has been cleared of any serious injury in a major boost for Australia, who seem set to be without David Warner (groin) and Will Pucovski (concussion) again for the Second Test in Melbourne starting on Boxing Day.
The Aussies enjoyed a stunning third day turn-around, bowling out India for only 36 inside 22 overs in the first session of the day with the pink ball.
Josh Hazlewood took 5-8 while Patrick Cummins got the ball rolling with the first three dismissals and finished with 4-21.
Paine was named Player of the Match for his tough 73no in the first innings which helped Australia narrow the gap, trailing by 53 runs at the halfway point.
India have a raft of issues moving forward, particularly after their deplorable second innings score, which was their lowest in their history.
Captain and star batsman Virat Kohli now heads home to be with his wife ahead of the birth of their first child, while Mohammed Shami was innings batting on day three to add injury to insult.
“I don’t think we have ever had a worse batting performance so we can only go upwards from here and understand as a team we can do special things when we think of partnerships and batting together,” Kohli said.
“I am very, very confident that we will bounce back strongly in the next one, and I have no doubts you will see guys stepping up and really realising their true character.”