When Ashwin pulled out of a delivery as Lyon was halfway through his run-up, Paine said: "We can't wait to get you to the Gabba, Ash."
Ashwin quickly responded: "Just like we want to get you to India. It'll be your last series."
Paine shot back: "Maybe, are you a selector here as well? At least my teammates like me, d***head I've got a lot more Indian friends than you do. Even your teammates think you're a goose. Don't they. Every one."
Matthew Wade was also heard on stump mic saying, "Just don't end up with a broken rib".
The remarks spurred Ashwin to pull out of another Lyon delivery, which evoked a chorus of boos around the ground.
Ashwin said: "Tell me when you're done."
Paine replied: "I can talk all day mate. You wait until you get to the Gabba pal."
After the next ball was bowled, Paine targeted Ashwin once again.
"How many IPL teams wanted you when you asked every single one of them to have you?" Paine continued.
"If you captain, 'Oh coming from captain'," he added with a mocking accent.
Paine continued two balls later: "I've already played a series in India … can't remember my average, 60 something."
On Fox Sports, former Test spinner Kerry O'Keeffe said: "It's not banter, it's pointed."
But Australian great Mike Hussey said it was "tactics, trying to put Ashwin off his concentration", adding that it was a sign of desperation.
Indian legend Sunil Gavaskar was less kind in his assessment.
"It's ridiculous. It's unnecessary. What he said he's got more friend than Ravichandran Ashwin is unwanted and unnecessary," Gavaskar said on Channel 7.
"This game has been such a fabulous game of cricket. I tell you what, what Tim Paine said to Ravichandran Ashwin just waiting to get you to the Gabba, I can tell you, Bumrah and company are also waiting to get to the Gabba."
The remarks soon came back to haunt Paine, as he dropped a catch off Hanuma Vihari the very next over.
While the Indians were being pummelled throughout the day as Australia banged it in short, Wade came underfire for seemingly mocking the visitors injuries as he fielded in short leg.
There was vision of Wade when he was fielding in close and knocked down a ball he appeared ready to charge the batsman before stopping to pick up the ball.
As his teammates patted him on the back, he mocked falling down injured.
On Channel 7, Michael Slater took aim at the move from Wade.
"I mean, Wade's just saying, look, I'm tough, I'm in here, I've been hit and I'm going to stand tall," Slater said. "You heard the batsman apologise for hitting him and he was making a step towards the batsman. I just think settle down, it's a tough position. He is getting hit. I don't go for this advancing towards the batsman when he is apologising for hitting you."
Fans were quick to slam the Aussie's intimidatory tactics.
The fourth and final Test will be juicy.
Vihari and Ashwin survived more than 40 overs at the crease together, denying the Australians a comfortable victory.