Bowling with a remodelled action, Ojha finished the day with figures of 3/52 as he had at one stage reduced Australia A from 57/1 to 75/4 in a space of 23 deliveries.
However Marcus Stoinis (42 batting) along with Peter Handscomb (75 batting) conjured an undefeated 110-run stand for the fifth wicket to stem the rot.
Earlier, India A were all out for 301 in their first innings after starting the day at overnight score of 221 for six.
While talented Tamil Nadu all-rounder Vijay Shankar (51) had an impressive 'A' team debut adding 62 runs for the seventh wicket with comeback man Amit Mishra (23), the last four wickets fell for a mere 18 runs as India A folded for 301 in 114.3 overs.
Also Read
Shankar on his part was unbeaten on 51 off 135 balls with five fours and a six.
When Australia A batted, opener Cameron Bancroft (20) nicked one off Abhimanyu Mithun to Naman Ojha behind stumps.
Skipper Usman Khawaja (25) and Travis Head (31) added an even 50 for the second wicket before Ojha ran through the top-order.
Head went as Mishra snapped him up off Ojha's bowling. In the 24th over, Ojha got two wickets as Khawaja was holed out at deep mid-wicket to Abhinav Mukund while Nic Maddinson was caught by Karun Nair.
However Handscomb played a patient unbeaten innings facing 137 balls in which he hit six fours. Stoinis, who had a contract with Delhi Daredevils during the last season of IPL, scored 42 off 87 balls with five fours and a six.