Chasing a modest 186, India were in doldrums at 5 for 68 before Pujara played the captain's role exceptionally well to guide the visitors to a nerve-wrecking win.
Pujara added 73 runs with number 10 batsman Shami Ahmed (27) to steer the Indians home after a spectacular collapse had severely jeopardised the team's chances.
Pujara, who has struck a 50 in the first innings, was once again patience personified as he held one end even as wickets tumbled at regular interval around him.
The 24-year-old right-hander faced 222 deliveries and struck 10 fours in a calculated innings that should impress the selectors when the senior squad is picked.
For the home team, lanky pacer Jason Holder, playing at his home ground, registered his third five-wicket haul in his 15th first-class match -- a performance that reduced India A to 115 for 8 at one stage.
On a rain-interrupted day, a draw seemed likely when the two teams went off the field in the final hour with India 'A' needing 20 runs but the weather cleared and Pujara ensured that it was an opportunity grabbed as he took his side to a nail-biting triumph.