Wade and Labuschange both misjudged his length and top-edged attempted pull shots. Wade was caught at mid-on in Natarajan's 13th over and Labuschagne, after surviving dropped catches on 37 and 48, was finally out for 108 after facing 204 deliveries when he skied one to wicketkeeper Rishabh Pant in the rookie bowler's 14th.
Natarajan finished the day with figures of 2-63 from 20 overs.
Australia all-rounder Cameron Green was unbeaten on 28 and captain Tim Paine was 38 not out at stumps.
The Gabba is a venue where Australia hasn't lost a cricket test since 1988. But for the second consecutive day of test cricket, India's gritty, injury-depleted lineup troubled Australia.
The Indians batted through the full final day in the third test in Sydney on Monday, losing only three wickets, to salvage a draw and keep the series level at 1-1 going into the last match.
A squad already missing injured veteran bowlers Umesh Yadav and Mohammed Shami and skipper Virat Kohli, who returned to India for the birth of his first child, had its depth tested even further when Bumrah (abdominal muscles), Ravichandran Ashwin (back), Ravindra Jadeja (thumb) and Hanuma Vihari (hamstring) were all ruled out for the Brisbane match.
Enter Natarajan and allrounder Washington Sundar for their first tests and the recalls for Shardul Thakur and Mayank Agarwal. India only need to draw at the Gabba to retain the Border-Gavaskar trophy, and has a relatively strong batting lineup.
But the inexperienced bowlers showed they're here to win.
Siraj led the attack in just his third test appearance and produced a breakthrough in the first over when he had David Warner (one) well caught by Rohit Sharma at second slip.
Thakur dismissed Marcus Harris (five) in the ninth over to make it 17-2, his first test wicket — he only bowled 1.4 overs in his only previous test after sustaining an injury.
Sundar also collected his first wicket — achieving it before he'd conceded a run — when he had former Australia captain Smith caught at short mid-wicket with his first ball in the post-lunch session after his morning spell contained three maiden overs.
Australia could have been in deeper trouble, but stand-in captain Ajinkya Rahane put down a routine chance at gully from Labuschagne when the hosts were 93-3.
Also souring that missed opportunity was a groin strain for the bowler, Navdeep Saini, which kept him out of the attack for the remainder of the day.
Here's how day one unfolded: