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.
Image: England's Monty Panesar celebrates the wicket of India's Virat Kohli with teammates during the third day of the second test match in Mumbai on Sunday