India lost Anil Kumble and Wasim Jaffer before reaching lunch on 75-3 on the fifth and last day while chasing a stiff 313-run target. Sachin Tendulkar was unbeaten on 34 at the break with skipper Rahul Dravid on nine.
The highest-ever total chased by a team to win a Test in India is 276, by the West Indies in Delhi in 1987.
India, who have added just 57 to their overnight total of 18-1, now need 238 more runs in 65 overs.
The tourists trail 1-0 in the series following their nine-wicket defeat in the second Test at Mohali. The opening match ended in a draw.
England's pace trio of Flintoff, Hoggard and James Anderson kept the batsmen subdued with their tidy bowling as the tourists strove to square the series.
Dravid has so far faced 57 balls for his nine runs, while Tendulkar looked uncertain early in his knock before playing a few handsome shots.
With runs hard to come by and two batsmen falling in the space of eight overs, India aimed at saving the game rather than going for the target. Just seven fours came off 25 overs in the two-hour morning session.
India lost nightwatchman Kumble in the day's third over, trapped leg-before by a Hoggard delivery which appeared to be missing the leg-stump. He failed to add to his overnight score of eight.
Jaffer (10) scored his first run after 23 balls when he square-drove Anderson for a four. But it turned out to be his only show of aggression before he fell soon afterwards, trapped leg-before in Flintoff's second spell.
Tendulkar, booed by his home crowd after his first-innings dismissal for one, took time to settle down against a disciplined attack. Early in his innings he survived a confident appeal for leg-before from Flintoff.
Flintoff tested Tendulkar with short-pitched deliveries and once came close to getting him out when a leading edge went past his outstretched right hand on follow-through.
Tendulkar then played a few attacking shots, on-driving and cutting left-arm spinner Monty Panesar for two fours in an over.