Agarwal sent the bowlers on a leather hunt with an unbeaten 220 off 250 balls while Shaw punished them with a well-made 136 off 196 balls during a 277-run opening stand.
India A now enjoy a 165-run lead after Mohammed Siraj took five for 56 to bowl out South Africa A for 246.
It was a day when India A openers scored runs at an average of 4.72 with an astounding 58 boundaries and five sixes.
Out of these, Agarwal alone hit 31 fours and four maximums. Shaw had 20 boundaries and a six in his seventh first-class hundred.
The hero of the day certainly was local boy Agarwal, who hit his eighth first-class century.
After a tremendous last season in domestic cricket where he scored well over 1000 runs, Agarwal continued his good form during the India A tri-series in England with three hundreds in List A tri-series.
"I think, I have seen the best knock from the blade of Mayank. He batted really well and I expect him to get more runs under the belt," Shaw told reporters after the second days play here.
On his knock, Shaw said:"I played according to the merit of the ball. When I saw ball to be it, I did simply that. I have been an aggressive batsman since my school days and I play my game as such," he said.
Both Shaw and Mayank played the morning session out and took the score to 122 or no loss after they had cracked a superb half centuries.
"The first session is very crucial or us. If you play that period in the morning, it is easier for the batsman afterwards because the ball comes nicely on to the bat. After that you can see our score kept moving," Shaw said.
Brief scores: India 'A' first inngs 411 for 2 in 87 overs (Mayank Agarwal 220 not out, Prithvi Shaw 136; Duae Olivier 1/69, Dane Piedt 1/56)
South Africa 'A' first inngs: 246 for 8 in 88 overs (Rudi Second 94, Sarel Erwee 47; Sarel Erwee 3/56, Navdeep Saini 2/47, Rajneesh Gurbani 2/47).
First Published: August 5, 2018, 7:44 PM IST