Pujara continued his patient approach at the beginning of the session before a flurry of boundaries took him to an unbeaten knock of 198.
England had shown signs of improvement from a tiring morning session to take two India wickets.
That brought MS Dhoni to the crease but after a 37-ball innings only resulted in five runs, he dragged an attempted sweep shot onto his own stumps to hand Swann his fifth wicket.
That appeared to hand England an opening to stamp some authority on the match but Pujara and Ravichandran Ashwin began to bat aggressively for the hosts and they quickly conjured up a 58-run partnership as the two teams went off for tea.
You can follow the final session of day two by following Sports Mole's live commentary.