Pujara, who had scored a double century in the first match, notched up his third Test century to remain unbeaten on 114 on a turning track at the Wankhede Stadium and steered the hosts to a far more comfortable 266 for six at close on an eventful opening day.
Pujara found an able ally in Ravichandran Ashwin (60 batting) as the duo put on unfinished 97-run partnership for the seventh wicket to bail them out after the hosts were reeling at 119 for five at one stage.
Barring Pujara and Ashwin, none of the batsman in the star-studded line-up could make an impression on a track that started turning from the second session onwards and which was exploited by left-arm spinner Monty Panesar who claimed four wickets.
Coming to the crease after the second ball dismissal of Gautam Gambhir, the 25-year-old Pujara kept one end going by showing superb judgement against the spinning ball to pull India out of a deep hole after the home team opted to bat first on winning the toss.
Pujara stayed for just over six hours in which he had faced 279 balls and struck ten fours. Ashwin faced 84 for his valuable knock.
Pujara came into the game on the back of his unbeaten knocks of 206 and 41 in the two innings of the opening Test at Ahmedabad, which fetched him the Man of the Match award and paved the way for his team's comprehensive nine-wicket victory.
Panesar, who took four for 91 by the end of the day's day, was played with a lot of assurance by Pujara.
It was the Rajkot-born youngster's third 100-plus knock in his last four Test matches, having scored a maiden century (159) against New Zealand in August.
Pujara, who has been dismissed only in the warm-up game for Mumbai A after making 87, continued to prosper against the visitors with his exemplary concentration and shot selection.
He gave one chance, when on 60, when he edged Panesar but James Anderson could not latch on to it.
When on 94, England needlessly appealed against him for a catch at midwicket, which was referred to the third umpire and the replays showed the ball had bounced in front of the short leg fielder.
The early part of the day belonged to England who sent back Gambhir (4), Virender Sehwag (30) -- in his 100th Test – Sachin Tendulkar (8), Virat Kohli (19) and Yuvraj Singh (0).
Barring Gambhir and Yuvraj, who fell to Anderson and Graeme Swann, the others were dismissed by Panesar.
Pujara and captain Mahendra Singh Dhoni, who mixed caution with aggression before becoming Panesar's fourth victim for 29, put on a partnership of 50 runs in 128 balls.
England's hopes of slicing through the Indian tail, though, came to naught with Ashwin scoring his second fifty.
With some more batting to come in the form of Harbhajan Singh -- drafted into the eleven as the third spinner after more than a year's gap -- Zaheer Khan and Pragyan Ojha, India would fancy their chances of taking the score past 300.
In the morning and soon after lunch, England applied the screws on India and made the hosts struggle on a turning track on which the ball gripped the surface and also bounced.
Panesar, who was left out of the first Test, was the destroyer-in-chief, with a splendid spell of 23 overs on either side of lunch for the wickets of Sehwag, Tendulkar and Kohli before coming on for another spell for the wicket of Dhoni.
Anderson and off-spinner Swann packed off Gambhir (4) and Yuvraj (2) in two balls apiece.
Gambhir, who flicked Anderson to midwicket off the first ball, missed the next to be rapped in front.
After pushing India on the back foot in the pre-lunch session, England continued the good work with a two-wicket burst in successive overs in the first hour of the post-lunch session.
Panesar, who sent back Sehwag and Tendulkar in successive overs before lunch, got his third victim by dismissing Kohli.
After disturbing the stumps of Sehwag and Tendulkar with sharply turning balls, Panesar induced Kohli to attempt a drive with a ball that drifted in and turned big on pitching to take the leading edge for Nick Compton to bring off a good diving catch.
Kohli had cover-driven the left-arm bowler and his spin partner Swann for attractive boundaries in successive overs before he was lured by the crafty Sikh.
The slow bowler made the ball drift in to the right-handers and extracted sharp turn off the track.
He could have had the confident-looking Pujara too when the batsman, batting on 60 in a team score of 135 for five, edged the bowler to the left of Anderson who could not latch on to the catch at short gully.
Had it been taken India would have been in deeper trouble.
Prior to this slice of luck Yuvraj, who made 74 on his Test comeback in Ahmedabad, had departed for a second-ball duck, clean bowled by Swann. Swann had been brought on for a new spell by skipper Alastair Cook soon after the left-hander arrived at the crease, and the move paid off.
The hosts lost these two wickets in successive overs for the addition of just one run to be tottering at 119 for five and the loss of Pujara, easily the best Indian batsman against the turning ball in this match, would have been a major blow to their hopes of putting up a fighting total.
Dhoni came to the crease and started to attack the two spinners with his drives and cuts.
He was lucky on 22 in a score of 149 for five when he stepped out against Swann, missed a big heave but luckily the ball clipped the top of his pad and got deflected before wicketkeeper Matt Prior could stump the batsman.
Dhoni was later out, caught off the gloves in the close-in cordon, off Panesar. Pujara and Ashwin, however, held fort.
Even the second new ball, taken after 80 overs, did not benefit England.
Pujara pulled Anderson for a four to complete his 100 in 248 balls, before Ashwin struck the bowler for three fours in an over to race to 50 in 67 balls.
The off-spinner has hit a century at this ground an year ago, against the West Indies.