With 154 overs and five sessions to survive for a draw, Brathwaite and Chanderpaul were cautious, taking few risks as they look to dig in for the long haul, cracking the occasional boundary with keeping wickets intact more important than runs.
Australia resumed at 29-1 with David Warner, who began on 17, the only wicket to fall, out for 48.
Labuschagne confidently built on his overnight three to reach a ninth Test century with Smith, who hit an unbeaten 200 in the first innings, not out 20.
In a setback for the West Indies, Kyle Mayers was unable to bowl with a right shoulder strain and Kemar Roach went off with a hamstring injury,
Adding to their injury woes, top-order batter Nkrumah Bonner was substituted out on day three with concussion after being hit on the helmet by a rising Cameron Green delivery.
But the pace of Alzarri Joseph and Jason Holder proved intimidating.
Labuschagne edged a six off Joseph before a huge let-off next delivery when a brutal short ball flew off his bat onto the side of his helmet and he was caught.
But a no-ball was called as he made his way off the field, with the batsman undergoing a concussion check before continuing on 19.
Warner and Labuschagne weathered the storm until spinner Roston Chase ended their 81-run partnership, with the veteran opener caught by Shamarh Brooks at short leg.
With runs flowing freely, Labuschagne powered to his century, from just 109 balls, and a slice of history to leave the West Indies with a huge task to save the game.