Australia resumed on 293-2 after dominating the opening day of the first Test between the sides in nearly seven years, with David Warner (5) and Usman Khawaja (65) the only wickets to fall.
Labuschagne began the session on 154 and Smith on 59 with the West Indies desperate for an early breakthrough.
But on an overcast day with good batting conditions, Smith hit a boundary off Kemar Roach’s opening over to signal his intent and they quickly brought up the 300.
Once again, the West Indies bowled with discipline and occasionally threatened, with Labuschagne lucky to escape after top-edging a pull shot off Jason Holder on 175.
Shouts of “catch it” went up, but the ball fell harmlessly in mid-wicket.
Labuschagne had a big let-off on 196 when wicketkeeper Joshua Da Silva spilled a chance from the spin of Roston Chase.
He was otherwise in charge and reached 200 with a boundary off Jayden Seales before he was caught by Da Silva after getting an edge off the part-time bowling of skipper Kraigg Brathwaite.
It ended a patient innings of 350 balls, with 20 fours and one six.
A masterful Smith was untroubled as he swept to his 29th century, off 194 balls, to equal the feat of legendary Australian Bradman, who only played 52 Tests to Smith’s 88.
Smith is now joint 14th on the all-time list with his next target the 30 of fellow Australian Matthew Hayden and Shivnarine Chanderpaul, whose son Tagenarine is making his debut for the West Indies in Perth.
Indian great Sachin Tendulkar’s 51 centuries remains the benchmark.