Centuries to Steve Smith and Marnus Labuschagne have put Australia in control of the second Test against Sri Lanka in Galle.

On a dominant day for the tourists, Labuschagne scored his first Test ton outside of Australia with 104, before Smith finished unbeaten on 109 with Australia 5-298 at stumps.

Smith's century marked his first since January 2021, when he brought up three figures against India at the SCG exactly 18 months to the day earlier.

Long regarded as Australia's best Test batters, Friday incredibly marked the first time Smith and Labuschagne have scored a century in the same innings together.

It came as they combined for a crucial 134-run third-wicket partnership that took the day away from Sri Lanka and gave Australia control.

Ravaged by COVID-19 in the lead-up to the Test, Sri Lanka's spinners endured a difficult day, with only debutant Prabath Jayasuriya having any real success with 3-90.

The left-arm orthordox spinner was the bowler to finally remove Labuschagne when he had him stumped, before getting Cameron Green LBW on the sweep for 4 and bowling Travis Head on 12.

But generally, Sri Lanka's spinners struggled for consistency with their lengths, offering up too many loose balls on a Galle wicket far friendlier for batting than in the first Test.

Smith in particular made use of the errors in length, driving superbly through both the covers and through mid-on.

While Australia's other batters had made a point to play square and quickly, Smith was patient and waited for loose balls before punching them down the ground.

Labuschagne was strong square of the wicket, cutting anything wide of the off stump and also willing to come over the top of the ball and sweep the spinners.

But the story could have been so different for Sri Lanka had Niroshan Dickwella not fumbled a simple stumping on 28.

Dickwella had all the time to catch the right-hander short of his ground, but the ball went to ground and Labuschagne was let off the hook.

At that point Australia were 2-78 after David Warner (5) and Usman Khawaja (37) went in the first session.

But Labsuchagne proceeded to hit two boundaries off the next over as he began to capitalise on the error.

Dickwella eventually stumped him 76 runs later, but by then the damage had been done.

AAP/ABC