The West Indies tail batted superbly on Friday and followed up in commanding fashion with the ball to stun Australia, who trail in the second test by 35 runs.
Leading 1-0 in the two-game series, the home side recovered from 24-4 to boldly declare 22 runs behind at 289-9 in the night session at the Gabba in Brisbane, after fast bowlers Kemar Roach (3-47) and Alzarri Joseph (4-84) inflicted maximum damage.
Having been bowled out earlier in the day after Kevin Sinclair (50) lifted the visitors to 311, the Caribbean batsmen had to tough out 7.3 overs under lights to reach the day's close at 13-1.
Opener Tagenarine Chanderpaul (4) was caught-behind by Alex Carey off Josh Hazlewood on the last ball before stumps, leaving captain Kraigg Brathwaite unbeaten on three.
"I feel really, really good to get the fifty on my debut," Sinclair said. "It's about sticking with the basics for us."
New opener Steve Smith, thrust into the role after David Warner's retirement, fell to Roach for six in the first over of Australia's innings when a seaming delivery was adjudged lbw on review.
But it was a double-strike by veteran Roach on the stroke of dinner to send Cameron Green (8) and Travis Head (0) on their way that sent shockwaves through the home dressing room and brought about a strategy change.
Mitchell Marsh (21) and Carey (65), who found fortune when his bails were hit but not dislodged, played at better than a run-a-ball before holing out while opener Usman Khawaja (75) set anchor.
Offspinner Sinclair (1-53) brought out a backflip when Khawaja edged to slip and the job of reducing the deficit was left to Cummins, who hammered a career-best 64 not out to provide cheer to the 29,216-strong crowd attending on Australia's national holiday.
Cricket Australia in 2021 stopped referencing "Australia Day" for matches played on January 26 - the 1788 date when the first fleet of British settlers arrived in Sydney - after a recommendation from its Indigenous advisory committee.
Earlier, the eighth-ranked tourists antagonised the world test champions with the bat for 18 overs after resuming from 266-8 overnight.
An untimely tumble left Roach (8) exposed to a simple run out, prompting Sinclair to attack spinner Nathan Lyon (2-81) and reach 50 with a majestic six over long-on before being stumped off the next ball to end the first innings.