The left-handed wicketkeeper batsman, playing his third Test match, hit 106 to help his side manage 328 in their first innings.
In reply, the West Indies reached 8-165 at stumps on day two, still trailing by 163 runs.
West Indies are aiming to level the series as they lost the first Test in Barbados by three wickets while the second Test in Port of Spain was drawn due to rain.
Wade’s vindicating century overshadowed the brilliant bowling performance of Shane Shillingford, who bagged six wickets for 119 runs, recording his maiden five-for in Tests.
Resuming the innings at 212-7, Australia lost Mitchell Starc (35) early in the morning.
Starc, who recovered the tourists from 169-7 with a 57-run stand with Wade, was run-out while scampering for an inexistent double.
Wade, with the overnight score of 22, moved on the anticipations in the company of Ben Hilfenhaus (19) but kept the strike frequently in his hands.
Serving some deliveries with a cautious approach, Wade switched on a show of blistering hitting and lashed flamboyant shots all over the ground.
Wade reached his century off seamer Kemar Roach, driving wide through cover to move to 103.
Stitching up 102 runs in the mutual cooperation, Wade and Hilfenhaus eventually fell to Shillingford in the same over.
Wade’s flawless vigil was studded with 10 boundaries and three massive sixes.
The West Indies’ innings began on a negative note with Kraigg Brathwaite caught by Ryan Harris off Hilfenhaus’ bowling in just the third over.
After the quick dismissal, Adrian Barath (29) combined with Kieran Powell (40) for a 61-run stand to steady the hosts.
West Indies VS Australia 3rd Test Scorecard
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