And Monty Panesar, the tourists' premier spinner, failed to turn the ball and may be criticised for a lack of variety as he returned figures of 0-105 from 27 overs.
India, who led England 5-0 when the seven-match one-day series was abandoned, will carry their momentum into the second Test, which starts in Mohali on Friday.
Pietersen will be especially disappointed after Flintoff had given his side the perfect start, inducing an out-of-form Dravid into edging behind in the third over.
But Tendulkar, predictably, settled in quickly and guided the hosts past 150 with a superbly-timed cut through gully off Flintoff.
Alastair Cook failed to collect a difficult chance at silly point offered by Tendulkar off Swann and Flintoff almost bowled Gautam Gambhir (66) via his inside edge with an unconventional one-armed delivery.
The batsmen were otherwise unruffled and soon negated the effect of Graeme Swann and Flintoff, which led to the introduction of Panesar and Anderson, who looked anything other than threatening initially.
TMS Close of Play - First Test, day five
But Anderson continued to probe outside Gambhir's off stump and his perseverance paid dividends when he angled one across the left-hander, who slashed loosely and was caught by a sprawling Paul Collingwood at gully.
It was an important breakthrough for England but they failed to maintain the pressure, allowing Tendulkar and VVS Laxman to get India's victory push back on track.
Anderson was driven beautifully by Laxman through the covers for four and then Tendulkar cut the seamer over the slips to the rope.
Laxman was in fine touch, lacing both Panesar and Flintoff through extra cover for boundaries and then the latter down the ground to the same effect.
India reached lunch on 213-3, 174 runs short of their target, and it seemed increasingly likely that they would reach it as Pietersen kept faith with Panesar.
Swann, by contrast, was turning the ball far more effectively and, when he gained some sharp bounce with his 10th ball after the re-start, Laxman presented Ian Bell with the most simple of catches at forward short leg.
Tendulkar was again on hand to steady the innings and a couple of fours off Panesar had the crowd jumping once more.
HIGHEST FOURTH INNINGS WINNING TOTALS
418-7 West Indies v Australia, Antigua 2003
406-4 India v West Indies, Trinidad 1976
404-3 Australia v England, Headingley 1948
387-4 India v England, Chennai 2008
369-6 Australia v Pakistan, Hobart 1999
362-7 Australia v West Indies, Guyana 1978
At the other end Yuvraj provided an indication of what was to come by driving and sweeping Swann for successive fours and then clubbing Panesar over mid-on for another.
Tendulkar pushed Flintoff into the off side for a single to record his 52nd Test 50 and then nudged Swann for his 1,000th Test run in 2008.
Flintoff did his best to knock Yuvraj out of his stride during a period of verbal jousting but the batsman's levels of concentration were admirable and he swept Panesar fiercely to bring up the 50 partnership.
Yuvraj was fortunate to survive a huge leg-before appeal when replays suggested a ball from Swann that crashed into his pads was destined for middle and leg.
He responded by bludgeoning a woefully short Panesar delivery for six over mid-on and the following over, Tendulkar slog-swept Swann for four.
At tea India were 304-4, 83 runs shy of the win, and they progressed serenely at the start of the final session.
Pietersen took the second new ball after 83 overs but neither Anderson nor Harmison proved problematic to the batsmen.
Tendulkar traded in singles and the odd boundary, while Yuvraj began illustrating his usual explosive tendencies.
With the result now inevitable, it was fitting that Tendulkar should hit the winning runs and reach three figures with a paddle around the corner for four.
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