After dismissing India for 327 in the first innings, England moved to a comfortable 178 for two in 65 overs before the stumps were drawn on the second day, with the visitors trailing by 149 runs.
At close, the left-handed Cook, who had scored a big century in the first Test, was unbeaten on 87. The more aggressive Pietersen was batting on 62 after a stay of 127 minutes during which he faced 85 balls and hit nine fours.
Cook batted for 251 minutes and faced 209 balls, striking a six and ten fours in the process
The third wicket duo has so far put on 110 runs in 186 balls. For the record, Cook has batted for 960 minutes in all in the three innings he has batted during the series.
With three more days left in the second game of the four-match series in which India are 1-0 ahead, a result is on the cards on a track that is aiding the spin bowlers.
England, though, looked to have a slight advantage with a settled and experienced pair at the wicket and some more batting to follow.
On a wicket where the spin duo of Monty Panesar and Graeme Swann ran through the star-studded Indian batting line-up in which Cheteshwar Pujara (135) and Ravichandra Ashwin (68) stood out, the trio of home team spinners looked largely clueless against the determined Cook and Pietersen.
Barring the twin strike by left-arm spinner Pragyan Ojha in the space of 11 balls just before tea, the home side's spin attack looked far less menacing than both Panesar (five for 129) and Swann, who ran through the tail today to end up with figures of four for 70.
