At lunch, India were 410 for four in 121 overs, after adding 83 runs in 31 overs to their overnight score of 323 for four.
Pujara was unconquered on 133 after having batted for nearly six sessions while Yuvraj was unbeaten on 72 after a stay of 174 minutes.
While the right-handed Punjara hit 16 fours in 274 balls, the left-handed Yuvraj had six hits to the fence and two over it off 140 balls.
In the morning, needing just two runs to reach his second 100 in only his sixth Test, the 24-year-old Pujara got them in singles in nine balls that he faced in the morning.
Yuvraj, the other not out batsman who had played his previous Test one year ago against the West Indies, also moved along from his last evening's score of 24 to complete his fifty after the first hour of play with a four off Graeme Swann.
The pair also completed their century partnership for the fifth wicket in 204 balls, to pile on more agony on the visitors. It was the second three-figure stand for India in the game, after openers Virender Sehwag