Dane Piedt and Beuran Hendricks took three wickets apiece to knock India out for 120, as SA A stretched their lead to 292 by stumps on day two.
After reaching 274-4 after day one, SA finished their innings on 346 all out, Khaya Zondo (24), Hendricks (17) and Heinrich Klaasen (29) adding to their overnight total before losing their wickets.
India A got off to the worst of starts through an unusual run-out on the first ball, setting them back at 0-1.
Hendricks (3-23) and Junior Dala (1-36) then teamed up to knock over the top five with 42 runs on the board, Shreyas Iyer top-scoring for his side with 31.
Piedt (3-32) then joined in on the action to throttle the visitors even further, removing India A captain Karun Nair on 15.
India A managed to pass the 100-run mark, but Piedt struck again with a double in the 32nd over, removing both Shahbaz Nadeem (21) and Mohammed Siraj (0), before Shaun von Berg took the final wicket.
Vijay Shankar put in a decent contribution of 26, before he retired hurt as the visitors were bundled out for 120.
South Africa A had a decent start to their second innings, as Stephen Cook (32) and Aiden Markram (34) put on 66 by the end of day two.
Day three will start at 9:30 am.