At lunch, the home team were 162-1 in their first innings, 375 runs behind England, after starting at the overnight score of 63-0 at the SCA Stadium.
Opener Vijay was unconquered on 57, after having faced 142 balls and hitting 2 sixes and 5 boundaries in his 224-minute stay.
Pujara, who joined Vijay at the fall of opener Gautam Gambhir's wicket in the second over of the day, had overtaken the opener to be 62 not out off only 86 balls. His 117-minute essay contained 12 fours.
The lone batsman to be dismissed was left-handed opener Gambhir, who fell in the second over to Stuart Broad, after which Vijay and Pujara held fort till the end of the first session.
More From This Section
When the third day's play commenced India were faced with the daunting task of adding 275 more runs to avoid following on behind England's massive first innings 537.
Openers Vijay and Gambhir had started well last evening to put on an unfinished half century stand, but the latter departed early today after adding just one to his overnight 28. He was dismissed in the seventh ball of the day.
Gambhir tried to turn the fuller length ball to the leg side but failed to connect and it rapped him bang in front of the stumps with India on 68.
Vijay and new batsman Pujara - who has in the past scored a triple century for Saurashtra in Ranji Trophy at this very ground, then took up the daunting task of replying strongly to England's third-highest ever score in India.
Pujara was confidence-personified from the first ball he faced, off-driving Broad for a sweetly timed four. With Vijay playing second fiddle, Pujara set about getting the runs - quite a few of them with excellently timed boundary hits.
The Rajkot-born batsman clipped Broad off his pads and then drove Moeen Ali off the firing line by striking him for two fours - a square cut followed by a twinkle-toed dance down the wicket for an on-drive.
(REOPENS DEL 17)
Broad gave way to Chris Woakes at the other end and he once struck Pujara on the back of his helmet by digging the ball in short.
Vijay, too, was lucky as his leading edge to an attempted flick off Ansari did not go to the cover fielder's hands. Barring these two incidents, the two batsmen were in control as 43 runs were added in 13 overs in the first hour of play.
The local star was quickly narrowing the run-gap with Vijay who was content to play the supporting role.
As is his wont Vijay suddenly went into the attacking mode and clouted Ansari for a second six over long on, to the same area where he hit his first, and followed it with a lofted four to long off.
In the very next over Pujara too reached the minor landmark by exquisitely driving Stokes to the cover fence. It was his 10th four and his half century came off only 74 balls and in 100 minutes.
Vijay survived some anxious moments against leg spinner Adil Rashid in the last over before lunch. India added 99 runs in 27 overs in the two-hour period.