Pecker is a key witness in the case against the former US president, who is accused of falsifying business records to cover up hush-money payment
Clarke, 27, stroked six fours and a six for his eighth Test hundred and also shared a 106-run stand with Cameron White (44), leaving the tourists just 74 runs behind India's first innings score of 613-7 declared.
At the break, Brett Lee was batting on four with Clarke.
It turned out to be a frustrating session for the butter-fingered hosts who dropped Clarke three times and managed just one wicket while conceding 103 runs.
The Australian vice-captain was dropped twice in his 90s with Venkatsai Laxman -- celebrating his 34th birthday -- failing to cup a sitter off Virender Sehwag (5-104) and Amit Mishra grassing another in the bowler's next over.
Clarke was also spilled on 31 by Ishant Sharma who failed to latch on to a simple chance at mid-on off Mishra.
Sehwag, India's only triple-centurion, had something to cheer when he bowled White to bag his first Test five-wicket haul.
White hit five fours and a six off leg-spinner Anil Kumble in his cameo 95-ball effort.
Clarke, who scored 151 on his Test debut against India in Bangalore in 2004, also shared a 73-run stand with all-rounder Shane Watson (36) to frustrate a tiring Indian bowling attack.
Clarke's effort came on the back of useful contributions by Matthew Hayden (83), Simon Katich (64), Ricky Ponting (87) and Michael Hussey (53).
Kumble (1-94) returned to bowl in the 15th over a day after needing 11 stitches for a deep cut he sustained on his left little finger after lunch on Friday.
Kumble, who once bowled with a broken jaw against West Indies in Antigua in 2002, picked his first wicket of the series when he had Brad Haddin (17) stumped by Mahendra Dhoni.
The veteran bowler went wicketless in the drawn opening Test at Bangalore and missed India's 320-run victory in Mohali with a shoulder injury.
The fourth and final Test will be played in Nagpur from Nov 6-10.
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