Pujara, expected to be in the Indian team for the November 15-19 first Test to be picked tomorrow, came to the crease before lunch and spent the entire second session and much of the third till he was out after a 262-minute stay at the crease at the DY Patil Stadium.
Pujara, who hit 11 fours in 184 balls, and Hiken Shah put on a stand of 163 runs for the third wicket in around four hours as the disciplined England bowling attack toiled hard but was unable to separate the two for 338 balls.
In large measure due to the duo's fine batting, Mumbai A, replying to the visitors' first innings total of 345 for nine declared, ended the day 113 runs behind England with one more day to go.
At stumps, Shah was holding fort after having batted for over four hours, faced 190 balls and struck nine fours and a six.
Mumbai A lost their skipper Suryakumar Yadav in the last over of the day of the bowling of James Anderson, who took the second new ball, for 17.
Pujara, lucky to be let off on 22 by Anderson at slip off left-arm spinner Monty Panesar just after lunch, went into a defensive mode in the second session before opening out a bit in the last.
The 24-year-old Saurashtra batsman, who has played five Tests so far, was finally consumed by the same bowler, as Anderson pouched the edge off the defensive bat.
Mumbai A crawled their way back in the afternoon session against a disciplined England bowling attack after starting their innings 45 minutes into the third day. They moved to 43 for one at lunch with opener Bhavin Thakkar out for five.
The home team inched to 110 for two at tea break by adding 67 runs in the middle session in 31 overs and lost opener Shikhar Dhawan (27), who was sent back by part-time off break bowler Joe Root.
Pujara batted the entire second session to add 24 runs to his lunch score of 14. In all, he hit just three fours and a lone boundary in this period.
He became ultra-defensive after being let off by Anderson while diminutive left-hander Shah was stroke-less and run-less for a long time leading to drying up of runs in the second session.
After his escape, Pujara totally eschewed risks after he had shown some sort of aggression in the pre-lunch session, driving and cutting the bowlers for a few boundaries.
The post-tea period saw both the batsmen coming of the shell and striking fours when non-regular bowler Patel came on for a spell.
Pujara first cut Graham Onions for his first boundary after 67 balls and hit Anderson for another four to reach his 50 in 140 balls and after 194 minutes stay at the crease, 11 overs into the final session.
He then struck Patel for successive boundaries to raise the 100 of the third wicket stand in 261 balls as the home team added 43 in 14 overs in the first hour post-tea.
Shah, rendered stroke-less by the accurate bowling, opened out a bit to reach his individual 50 with a couple off Patel in 140 balls, containing four fours.
In the morning, Mumbai A new ball bowlers Shardul Thakur and Kshemal Waingankar polished off three tourists batsmen for the addition of seven runs.
Thakur bagged two of the three wickets that fell before England declared their innings closed at the fall of Graham Onions to Thakur in the last ball of the eighth over.
Thakur, who finished with three for 53, sent back left-handed Broad, who fell leg before, and Onions, who was caught behind, in the space of 12 balls.
Waingankar packed off overnight unbeaten batsman Samit Patel, who added just one run, to add to the two wickets he grabbed yesterday for innings figures of three for 72.
Patel, who was caught behind to the 12th ball he faced, hit seven fours in his 110-minute innings. Broad and Patel were out in successive balls in consecutive overs and at the same score of 339.
England declared when Onions departed with Monty Panesar yet to bat. The visitors lost three wickets in 23 balls in the morning after resuming at 338 for six.
Apart from Waingankar and Thakur, seamer Javed Khan (2 for 75), who turned up to play yesterday hours after his father died and also missed the funeral held in the morning, and captain Suryakumar Yadav (1 for 30) were the other wicket takers.