According to supersport.com website, Cook (87 not out) and Pietersen (62 not out) combined for 110 runs to draw the tourists to within 149 runs of India's first-innings total, having bowled the hosts out for 327 earlier in the morning.
Monty Panesar ended Ravichandran Ashwin's innings on 68 to seal his 11th five-wicket Test haul, before Graeme Swann mopped up the rest of the wickets, including that of Cheteshwar Pujara for 135, his first dismissal of the series after more than 1 000 minutes of batting.
Ashwin was trapped by Panesar's arm ball, while Swann beat Harbhajan Singh (21) for his 200th Test wicket, before turning the ball past Pujara for Prior to remove the bails.
Zaheer Khan was unlucky to be given out to a bat-pad decision by Umpire Aleem Dar as the ball missed the bat by several inches. It left India a four-over spell to Test England before lunch.
After the break, Nick Compton fell to Ojha for 29 and Jonathan Trott departed soon after, also to Ojha.
Harbhajan could have been given the wicket of Cook after the skipper missed the ball playing across the line on 84, but, having been given not out, Hawk-Eye showed another on-field umpiring error. Without the DRS being utilised, India were simply left to rue their bad luck.
Cook and Kevin Pietersen each close on their 22nd Test centuries - both would then share the record for an England batsman should they reach the landmark, alongside Wally Hammond, Colin Cowdrey and Geoffrey Boycott.