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Australia were still 295 runs behind India's imposing first innings total of 469 all out after a spectacular batting collapse on a good Mohali pitch.
Mishra, 25, playing due to skipper Anil Kumble's injury, took three for 42 while paceman Ishant Sharma took two.
Australia all rounder Shane Watson was on 32, holding one end up for over two hours, and Brett Lee was on five as India took command to push for a lead in the four-test series. Australia, reduced to 104 for two overnight replying to India's first innings 469 all out, had pinned their hopes on the consistent Mike Hussey and Watson.
But after Australia's top order collapsed on the second evening, any hopes of staging a recovery quickly vanished.
Watson and the 33-year-old Hussey, who top-scored with 146 to help the tourists dominate the drawn first test, faced testing spells from the right-left pace duo Ishant Sharma and Zaheer Khan in the morning.
RISING STATURE
Hussey, on 37 overnight, took a couple off Sharma to reach his 10th fifty only to be succumb two balls later to sharp reverse-swing bowling with the old ball by the long-haired Delhi bowler.
Hussey edged the next two deliveries from Sharma, which moved away from the left-hander. The first one speeding past slip for four but the next provided wicketkeeper Dhoni an easy catch.
His three-hour effort included seven fours.
The 20-year-old Sharma took two for 48 to continue his rising stature in the Indian ranks.
Harbhajan Singh replaced Sharma and struck in his second over when he bowled Brad Haddin (9) with a flighted off break that knocked back off-stump, reducing them to 146 for six. Mishra then bowled Cameron White with a tossed up googly to claim his third wicket and expose the tail. Australian openers Matthew Hayden (0), skipper Ricky Ponting (5), Simon Katich (33) and Michael Clarke (23) fell early to bring the world number one team under pressure on day two.
Saurav Ganguly top-scored with 102 for his 16th test century in his farewell series and raised partnerships of 142 runs and 109 runs with Sachin Tendulkar (88) and stand-in skipper Mahendra Singh Dhoni (92) to guide India to a solid first innings total.
The first match of the four-test series ended in a draw.
Scoreboard at lunch on the third day of the second test between India and Australia at Mohali, India, on Sunday.
India first innings: 469 all out (G.Gambhir 67, S. Tendulkar88, S.Ganguly 102, M.Dhoni 92, Siddle 3-114, Johnson 3-85)
Australia first innings (overnight 102-3)
M.Hayden b Khan0
S.Katich b Mishra33
R.Ponting lbw b Sharma5
M.Hussey c Dhoni b Sharma54
M.Clarke lbw b Mishra23
S.Watson not out32
B.Haddin b Harbhajan9
C.White b Mishra5
B.Lee not out5
Extras: (lb-4 nb-4)8
Total: (for seven wickets, 66 overs) 174
Fall of wickets: 1-0 2-17 3-62 4-102 5-130 6-146 7-167
To bat: M.Johnson, P.Siddle.
Bowling (to date): Khan 20-6-46-1 (nb-), Sharma 15-4-48-2 (nb-1), Harbhajan 17-6-34-1 (nb-1), Mishra 14-2-42-3 (nb-1)
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