After gaining the upperhand over their rivals in the two days, forcing the visitors to follow on, India 'A' bowlers had to face stiff resistance from the visiting batsmen with North playing a match saving innings.
Australia made 263 for seven in their second knock, gaining a 95-run second innings lead, before the match was called off after the first over in the final hour of the match.
Medium pacer S R Tyagi was the most successful bowler for India in the second innings, claiming four wickets for 42 runs with all his wickets coming in the second spell, which read 7-2-21-4, while off spinner Manish Parmar took two for 55.
Earlier, reeling at the overnight score of 113 for eight, still needing 22 runs to avoid follow on, Australia 'A' lost its remaining two wickets after adding just three runs, chasing India's first innings total of 284.
Parmar, who was the most successful bowler for India with a match figure of six for 92, sent back George Bailey, caught by Rahane in the short-leg after adding just one run to his overnight score of 37.
Piyush Chawla took his third wicket of the innings by trapping Bryce McGain (0) to put an end to the Australian innings at 116.
With nearly a full day left in the game, Australians needed to play with much more application than they did in the first knock when they were struck on their backfoot against the Indian spinners and paid the price.
Philip Hughes (43) and skipper Simon Katich, who hit a half- century making a fighting 56 (7x4, 1x6), laid a good foundation adding 88 runs in 20.5 overs. Indian skipper S Badrinath, bowling his off-spinners, rattled the stumps of his counterpart after Parmar had drawn the first blood sending back Hughes.
Australia then lost the wicket of Adamn Voges (9) to be down at three for 144, but North, who was joined by George Bailey (29), added 88 runs for the fourth wicket in 30.3 overs to scuttle the Indian charge.
North hit 10 well-timed hits to the fence and also succeeded in neutralising Chawla and Parmar, who had threatened to run through the Aussie innings. Tyagi had the last laugh when he had North caught by the Indian skipper in the mid-on when he failed to properly connect a heave off the medium pacer.
Brief scores: India A: 284. Australia A: 116 and 263 for seven (P Hughes 43, S Katich 56, M North 88, G Bailey 29, S R Tyagi 4/42, M Parmar 2/55).