Pietersen made 186 while Cook hit 122, his second successive ton in the series. Captain Cook had scored 176 in second innings of first Test in Ahmedabad.
England were all out for 413, with a lead of 86 runs. Later, India were reduced to 117/7 in second innings as Monty Panesar took five wickets.
Here are the images from third day.
Another century for captain Cook
Alastair Cook raises his bat after completing his second successive century.
Brilliance of Kevin Pietersen
Kevin Pietersen plays a shot en route to his 22nd Test century in Mumbai on Sunday.
Pietersen on the sweep
Kevin Pietersen sweeps during his knock of 186.
Finally, Ashwin strikes
R Ashwin celebrates a wicket on Sunday.
Indian players rejoice
Indian players celebrate an England wicket on Sunday.
Five wickets for Ojha
Pragyan Ojha roars after getting his fifth wicket on Sunday.
Monty Panesar spins India into trouble
Monty Panesar dismisses Yuvraj Singh on Sunday. Panesar took five wickets to put England on top. India ended day four at 117/7, lead of just 31 in second innings.