Pietersen (186) and Cook (122) notched up their 22nd Test centuries in a masterly exhibition of batsmanship on a turning track as England folded up for 413 just at the stroke of tea before reducing the hosts to a precarious 117 for seven at close on the third day.
After conceding a 86-run lead, India's top order batsmen surrendered rather tamely to the English spinners who exploited the conditions far better than their Indian counterparts who inexplicably lacked the sting.
Gautam Gambhir (53) and Harbhajan Singh (1) were at the crease with India just 31 runs ahead on a day which saw as many as 15 wickets fall on a Wankhede pitch giving ample assistance to the spinners. Virender Sehwag (9), Cheteshwar Pujara (6), Sachin Tendulkar (8), Virat Kohli (7), Yuvraj Singh (8) captain M S Dhoni (6) and R Ashwin (11) were back in the pavilion much to the disappointment of a huge Sunday crowd.
Monty Panesar, who claimed five wickets in the first innings, was the chief destroyer with another five-for as India's famed batsmen fell prey to the left-arm spinner who extracted a lot of spin and bounce.
The day clearly belonged to Pietersen and Cook who tilted the balance in England's favour with a record 206-run partnership for the third wicket, eclipsing the previous record of 144 between Mike Gatting and Allan Lamb in 1984-85.
Cook, who struck his second successive century, anchored the innings while Pietersen was the more aggressive partner as the pair frustrated the Indian spinners. Pietersen never allowed the spinners to settle down as he kept the score moving with a flurry of shots.
But the England innings collapsed after the dismissal of Pietersen, with the last six wickets falling for just 56 runs. Pragyan Ojha was the pick of the Indian bowlers with five for 143 while Harbhajan Singh and Ashwin chipped in with two wickets apiece.
India sliced through the England innings after Cook was dismissed. With their efforts, both Cook and Pietersen joined Walter Hammond, Colin Cowdrey and Geoff Boycott who hold the record for the maximum Test tons for England.
The duo's double century-stand assumed more significance after the last eight English wickets fell for 139 runs.
Ojha had figures of five for 143, his second fifer in as many Tests.
England lost their last four wickets in a heap, for the addition of just seven runs, once wicketkeeper Matt Prior was run out at 406.
The tourists, who resumed on 178 for two overnight, were dismissed eight minutes before tea. The England skipper departed when he edged Ashwin to Dhoni who later caught Pietersen off Ojha in the second hour after lunch.
Cook's departure before lunch triggered a collapse in which seven wickets fell in quick succession.
Once the Cook-Pietersen partnership was broken, Ojha got into his wicket taking act with a spell of three for 52 on either side of lunch during which he sent back Jonny Bairstow (9), Samit Patel (26) and Pietersen, who struck 21 fours and four sixes in his 233-ball knock in 317 minutes.
Ojha had accounted for Nick Compton and Jonathan Trott yesterday. But Pietersen was especially harsh on Ojha who foxed him twice at Ahmedabad.
Ashwin captured the wicket of Cook while Harbhajan Singh, the third spinner in the team, struck late in the session to send back Stuart Broad caught brilliantly at silly point by a diving Pujara, and then trapped James Anderson in front.
England, who put on 120 runs at a quick pace before lunch, added 115 off 27 overs after the break.
The Indian second innings started badly. Unable to negotiate the ball that was made to spin viciously by the two England spinners, India lost the wickets of Sehwag, Pujara and Tendulkar to be reeling at 52 for three.
Sehwag and Tendulkar, who failed for the third time in the series in as many attempts, were consumed by the crafty Panesar in his fourth and eighth overs while Graeme Swann sent back first-innings centurion Pujara, who failed for the first time in the series.
All three were dismissed while trying to defend – Sehwag and Pujara were caught in the close-in cordon around the bat and Tendulkar was trapped in front while playing across to Panesar.
The veteran batsman has a sequence of 15, 8 (Perth), 25, 13 (Adelaide) against Australia; 19 (Hyderabad), 17, 27 (Bangalore) against New Zealand; 13 (Ahmedabad), 8 and 8 (in this game) to show for in his last 10 innings.
England packed off Kohli when he hit a dipping full toss from Swann to cover fielder, substitute Joe Root.
Yuvraj was caught bat-pad off Panesar who then got rid off Dhoni whose edge off a turning ball was taken at slip.
In the morning, Cook notched up his second century on the trot in his calm and collected fashion while Pietersen hammered his way to 186 to put England ahead.
Starting the day at 87, Cook reached his second hundred of the rubber following his marathon effort of 176 in the second innings of the opening game at Ahmedabad, while Pietersen notched his first of the series as England batted their way to within 29 runs of the home side's first innings total of 327 when India broke the stand.
Ashwin brought an end to the double century partnership by sending back Cook and then Ojha claimed Bairstow, through a controversial catch, on the stroke of lunch to bring back the home team back into the picture after Cook and Pieternsen dominated the proceedings.
Bairstow was given out caught off the last ball though it struck the batsman's hand, hit the grille of his helmet and bounced back into the fielder's hands at silly point. The batsman walked off soon after Gambhir caught the ball on the second attempt.