The home team's number three came to bat in the fourth over at the fall of David Warner's wicket and batted throughout the day, facing 270 balls and striking 16 fours and a six.
Opener Usman Khawaja hit 65 and shared in a 142-run stand with Labuschagne for the second wicket.
Labuschagne survived chances on 75 and 137 brought up his eighth Test century inJayden Seales bowled left-handed Warner for just his 29th match with Steve Smith unbeaten on 59 at he close of play.
The Windies started well with the ball as paceman Jayden Seales bowled left-handed Warner for just five after Australia captain Pat Cummins had won toss and decided to bat first.
Khawaja and Labuschagne then took control of proceedings with the former going to his 18th half-century in his 52nd Test.
The left-hander was though undone by a beautiful delivery from Kyle Mayers, edging the seamer to wicketkeeper Joshua Da Silva in the second session.
Smith looked in good fettle with the bat and reached his 37th Test fifty and will doubt be eyeing another century on Thursday to draw level with the great Donald Bradman on 29.
The Windies handed a debut to batter Tagenarine Chanderpaul, the son of retired great Shivnarine, and will need to big performance with the ball on day two to get back into the contest.