Mishra, 24, sent back Simon Katich (33) before dismissing Michael Clarke (23) off the penultimate ball of the day to reduce the visitors to a shaky 102-4 on what still seemed a good batting wicket.
His efforts with the ball came after Sourav Ganguly hit a century and Mahendra Dhoni an attacking 92 to take India to 469 all out in the first innings.
At stumps, Michael Hussey was on 37 with five fours.
It was Zaheer Khan again who gave the home side the crucial breakthrough when he cleaned the off-stump of opener Matthew Hayden for a duck off just the third ball of the Australian innings.
It was the third time in the series that the left-arm paceman claimed Hayden cheaply after dismissing him twice in the drawn Bangalore opener.
Australian captain Ricky Ponting fumbled around for nearly half an hour for his five runs before being trapped leg before by a sharp incutter from new-ball bowler Ishant Sharma.
Katich looked in good touch, reading both the seamers and the spinners well until he misjudged Mishra and gifted him his maiden Test wicket.
His 65-ball knock contained six fours, including three of them off Sharma.
Australia would have been in deeper trouble had Dhoni taken a simple catch off Hussey off Harbhajan Singh when the batsman was on 25.
Earlier Ganguly, aged 36, hit eight fours in his patient 225-ball knock and shared a 109-run partnership with Dhoni, who hammered eight fours and four sixes in his entertaining 124-ball innings.
Ganguly, set to retire after the four-Test series for the Border-Gavaskar trophy, reached his 16th Test century with a four to the square leg fence off leg-spinner Cameron White.
The former Indian captain, who completed 7,000 runs in his 111th Test on Friday, was out soon after reaching his century, holing out to Brett Lee at long off to give White his first wicket of the match.
White (2-71) struck again when he cleaned the off-stump of Harbhajan to reduce the home side to 442-8.
Dhoni though continued his attacking style of batting, pulling Lee twice over square leg for fours as the paceman struggled with his line and length once again in the morning session.
Lee (1-86) also needed two stitches on his right hand after hurting himself while stopping a ball in his follow through.
Dhoni, leading the side in the absence of injured captain Anil Kumble, was also severe on debutant fast bowler Peter Siddle, pulling him over fine leg for the first six of the innings.
Dhoni's fiery knock was brought to an end by Siddle, who trapped him leg before with a searing inswinger, while Zaheer was run out by Lee.
Australia paceman Mitchell Johnson finished with 3-85 while Siddle also picked up three wickets for 114 runs from 28 overs.
The Mohali Test will be followed by matches in New Delhi and Nagpur.