India A lost their three top batsmen midway into the opening session for just 43 runs but Tiwary and Ojha rescued them with fine innings. One-down Jiwanjot Singh also played a part with a 56 after India elected to bat.
Tiwary shared a 134-run stand for the fourth wicket with Jiwanjot to take the visitors out of the wood. After Tiwary was out at 191 for five, his 118-ball innings laced with 12 fours and a six, Ojha took over to steady the Indian innings and took them to 304/6 at stumps at Allan Border Field here.
Ojha first paired up with Karun Nair (26) for a 63-run stand for the sixth wicket and then stitched 50 runs with Dhawal Kulkarni (12 batting) for the unbroken seventh wicket.
Ojha's 115-ball unbeaten innings was laced with 12 fours and a six.
Earlier, Tiwary's decision to bat first seemed to be backfiring with Robin Uthappa (23) and Lokesh Rahul (15) posting just 35 runs for the opening wicket.
Rahul was the first to go in the 10th over LBW off the bowling of pacer Ben Cutting after hitting three fours in his 31-ball innings.
Uthappa followed suit four overs later, falling victim of another pacer Mitchell Marsh to leave India at 43 for two. Ambati Rayudu (0) struggled in his short nine-ball stay at the crease and he did not trouble the scorers. He left India in a spot of bother before Tiwary and Ojha played the rescue act.
For Australia A, Cutting, Marsh and leg-spinner Cameron Boyce took two wickets each.
Brief Scores: India A: 304 for 6 in 89.1 overs (Manoj Tiwary 83, Naman Ojha 82 batting; Mitchell Marsh 2/46).
Image: Manoj Tiwary
Photograph: Matt Roberts/Getty Images
Tiwary, Uthappa named India 'A' captains for Australia tour
Shakib is MVP of rain-hit India-Bangladesh ODIs
Faulkner to lead Australia 'A' in 4-day series against India 'A'
Mohit, Binny bowl India to series win over Bangladesh
IPL PHOTOS: Yusuf slams fastest 50 to guide KKR to second spot