Ashwin didn't seem ruffled and provoked as he and Vihari remained unseparated after putting on 62 pricesless runs for the sixth wicket as the match ended in a draw.
With this draw at the Sydney Cricket Ground (SCG), the four-Test series remains levelled 1-1, with the fourth and last match starting on Friday.
On a couple of occasions during India's second innings, Ashwin was seen backing away from his stance and looking at Paine during Nathan Lyon's over as the Australia wicketkeeper-captain tried to break his concentration while the game progressed towards a draw.
In the 122nd over, Paine was heard on the stump mic saying: "Can't wait to get you to the Gabba, Ash". He was referring to the Indian team's reluctance to travel to Brisbane for the fourth Test due to the hard quarantine rules in that city, though on Monday it was confirmed that the Test would be played in Brisbane as scheduled.
Ashwin replied: "Just like we wanna get you to India, may be your last series."
"Even your teammates think you're a goose. Don't they? Every one of them. How many IPL teams wanted you, when you asked every single one of them to have you?" Paine further told the all-rounder.
Ashwin's wife Prithi was amused by the conversation and tweeted: "Where to get full transcript of conversations from stump mics."
Chasing a mammoth target of 407, India reached 334/5 batting for 131 overs before both teams decided to shake hands during the final session of the day.
Ashwin scored an unbeaten 39 off the 128 deliveries and along with an injured Hanuma Vihari -- who was barely able to move due to injury -- he shared an unbeaten 62-run partnership, while batting for more than 40 overs and prevented the hosts from taking a 2-1 lead. Vihari, batting with an injured hamstring, remained unbeatne on 23, scored off 161 balls.