Pujara cracked 17 fours in his 205-ball innings and forged a 176-run partnership with Rohit Sharma (70) for the third wicket to put India A in a solid position in the four-day match.
Pujara, who won the toss and elected to bat, also added 66 runs for the second wicket with opener Murali Vijay (44) at Olympia Park.
The Saurashtra batsman was ably supported by Sharma, whose unbeaten 159-ball innings was studded with eight fours and a six.
At stumps, Sharma and Ajinkya Rahane (11) were at the crease.
Earlier, opener Shikhar Dhawan (11) took time to see off the initial phase but the Delhi batsman could not stay longer at the crease, getting dismissed by Simon Harmer.
Harmer induced a edge from the left-handed batsman to Reeza Hendricks at first slip. Dhawan had just one six to show in his 46-ball innings.
Vijay, however, looked in good touch right from the beginning and along with Pujara steadied the ship after the fall of Dhawan.
He was dismissed by Andrew Birch when he had him caught by Harmer at second slip in the 38th over. His 115-ball innings was laced with six fours and a six.
Pujara and Sharma then joined hands and kept their opposition busy, picking up singles and twos and also put away the bad balls for boundaries.
The duo made the South Africa A bowlers toil hard and took India A to 147 for two at tea.
After the break, Pujara and Sharma kept the scoreboard ticking and had no problem in getting boundaries. Both the batsmen picked up seven boundaries each and scored 123 runs between them.
Pujara was finally dismissed when he played and missed a delivery from Wayne Parnell in the 84th over as India A slipped to 270 for three.
Earlier, Vijay started the proceedings with a cover drive off Parnell in the second over. He picked up another boundary off Birch in the 14th over.
The Tamil Nadu batsman gave a special treatment to Harmer as he smacked a four and a six in successive deliveries of one of his overs.
The 29-year-old repeated his act in the 23rd over by Harmer when he first drove one through covers and then swept another delivery to the boundary.
Harmer was also at the receiving end of Pujara when the Saurashtra batsman pulled him over square leg and then cut him through the point region in his consecutive overs.
Pacer Abbott too bled runs as both Pujara and Vijay picked up a boundary each off his overs.
Pujara went berserk and cut Parnell through point and gully area before picking up another four at the point region. In the 35th over, he once again stole runs off Abbott when he flicked him to the fine leg region.
Birch gave the hosts the much-needed breakthrough when he had Vijay caught by Harmer at second slip in the 38th over.
Rohit Sharma then joined Pujara in the middle and just before the drinks, the skipper sent Birch across the fine leg area for another four.
Sharma picked up his first boundary too against Birch when he drove him across the cover region.
Pujara reached his half-century when he edged a Birch delivery but it fall short off the gully fielder and raced away to the boundary.
Sharma then picked up a six off Harmer over mid-on as India A reached 121 for two in 50 overs.
Pujara hit boundary off Parnell and then sent Duminy through the covers for another four in the 58th over just before the tea break.
After the interval, Pujara and Sharma continued their good run and didn't allow the bowlers to dominate in anyway.
In the 73rd over, Sharma and Pujara reached their personal milestone as they completed their half-century and century.
It was Sharma who took a singles first to reach his fifty and then Pujara brought up his century when he took a couple of runs off Harmer.
Parnell finally took the wicket off Pujara but by then it was too late.