Australia has taken a 1-0 series lead over Sri Lanka with a convincing win by an innings and 40 runs inside three days at the Gabba.

Pat Cummins played destroyer-in-chief with superb figures of 6-23 as Sri Lanka crumbled for 139 runs, giving Australia its second Test win of the summer after a disappointing four-Test series against India.

It means Australia is well and truly in the box seat to reclaim the Warne-Muraliduran Trophy, with only February's Test at Manuka Oval remaining.

After getting the first wicket of Sri Lanka's second dig on the very last ball of day two, Cummins picked up where he left off, dismissing Dinesh Chandimal (0) with his second ball of the day as the batsman edged a sharp catch to Kurtis Patterson at gully.

In Cummins's next over, another wicket fell as the dangerous Kusal Mendis edged to Joe Burns at slip for just 1.

Burns would get a second — and even better — catch at slip thanks to Cummins, as Roshen Silva's (3) drive nicked to the cordon, forcing Burns to dive forward to pouch a brilliant take, with Sri Lanka reeling at 4-35.

Dhananjaya de Silva (14) hung around for a bit as he and Lahiru Thirimanne looked to consolidate, but de Silva would be dismissed by the ball of the day to cripple Sri Lanka's innings.

That ball was delivered by debutant Jhye Richardson, who took some of the limelight off Cummins with a gorgeous swinging delivery pitched just short of yorker length, beating de Silva's front-foot defence to castle the off stump.

Thirimanne would fall for 32 soon after the resumption of the second session, edging Cummins to Paine to secure the bowler's fourth career five-wicket haul.

Sri Lanka burned a review on the dismissal, but Snicko appeared far from conclusive with the noise off the bat coming a frame after the ball looked to pass the bat. Nevertheless, the dismissal stood.

The last real resistance for Sri Lanka fell with Niroshan Dickwella's dismissal for 24, as he fell straight into the trap set for him by captain Paine, hooking Richardson straight at the well-positioned Marcus Harris behind square leg.

Cummins had some help from Patterson to complete his 10-wicket haul for the match when he found the edge of Dilruwan Perera's bat and the ball flew towards gully, where Patterson leapt to his right to take an absolute screamer of a catch.

Kurtis Patterson took one good catch and one great catch on day three at the Gabba. ( AAP: Darren England )

That left him in a race with the wicketless Mitchell Starc for the final scalp, but it was the spin of Nathan Lyon that ultimately ended the match when Suranga Lakmal ran past a ball and was comfortably stumped for 24.

The tourists were left stranded on 9-139, with seamer Lahiru Kumara unable to bat with a torn hamstring that has rubbed him out for the second game in Canberra.

Check out how the victory unfolded in our live blog below.