Australia 414 (Carey 156, Smith 131, Jayasuriya 5-151) and 75 for 1 (Khawaja 27*, Labuschagne 26*) beat Sri Lanka 257 (Kusal 85, Chandimal 74, Starc 3-37) & 231 (Mathews 76, Kusal 50, Kuhnemann 4-63, Lyon 4-84) by 9 wickets
Steven Smith completed an outstanding series at the helm with his 200th Test catch, but he wasn't needed with the bat as Australia clinically sealed a rare series victory in Asia early on day four.
After wrapping up Sri Lanka's second innings within the opening 20 minutes of the day's play, Australia only lost opener Travis Head in pursuit of the 75-run victory target to win the second Test by nine wickets and sweep the series 2-0.
Usman Khawaja, who set the tone with a double century in the first Test, finished unbeaten on 27 while Marnus Labuschagne made a fluent 26 not out in a confidence boost with his place in the side attracting some scrutiny.
Frontline spinners Matthew Kuhnemann and Nathan Lyon claimed four wickets apiece in Sri Lanka's second innings to cap their brilliant series. They combined to take 30 of the 40 Sri Lankan wickets in the series.
It was Australia's first Test series victory in Sri Lanka since 2011 having lost four of five matches across the 2016 and 2022 tours. Australia's only other series victory in Asia since 2011 was in Pakistan three years ago.
The only concern for Australia will be the fitness of Smith, who looked sore in the field in what might be an aggravation of an elbow injury that he suffered ahead of the series in the BBL. But he remained on the field and was padded to bat.
Sri Lanka's hopes of setting a tricky chase rested entirely with Kusal Mendis, who had raced to 48 in a counterattack late on day three. Resuming at 211 for 8 with a lead of 54, Sri Lanka promoted Lahiru Kumara to No. 10 after he survived 26 balls in the first innings in a 33-run last wicket partnership with Mendis.
Mendis on his second delivery of the day's play reached his second half-century of the match, but he fell two balls later to vicious bounce from Lyon as a top-edge ballooned to fine-leg where Smith became the first Australian to claim 200 Test catches.
With Sri Lanka's hopes dashed, the only remaining interest centered on whether Kuhnemann or Lyon would finish with a five-wicket haul. Lyon had two big lbw shouts on Nishan Peiris turned down by umpire Adrian Holdstock as Australia reviewed unsuccessfully.
Lyon's frustrations grew after Kumara edged low down to Beau Webster at second slip only for replays to show it didn't carry. Webster took it upon himself to end the innings when - just like late on day three - he unfurled his offspin and clean bowled Kumara on his first delivery.
It completed a strong allround match for Webster, who showcased his versatility with the ball and he also took several sharp catches.
Desperately needing early wickets, skipper Dhananjaya de Silva went straight to his offspinners and Peiris produced sharp spin, but Head pounced when the bowlers missed their lengths.
After a nervous start, Head whacked Ramesh Mendis down the ground before Khawaja hit a couple of boundaries as Australia started to cruise. De Silva had to quickly resort to left-arm spinner Prabath Jayasuriya, who promptly dismissed Head off the top-edge.
With just 37 runs needed, there wasn't a lot to gain for Labuschagne who had missed out in this series amid a century drought stretching back to the 2023 Ashes.
He eased his nerves with a superb drive to the boundary and he whacked another off Jayasuriya to bring up Australia's 50. After a tough tour, Labuschagne had the satisfaction of hitting the winning run as Australia celebrated their first clean sweep in Asia since beating Bangladesh 2-0 in 2006.
Contests between the teams in Sri Lanka had been traditionally competitive, but Australia flipped the script with consecutive ruthless performances that felt out of the Steve Waugh era.
Their selections worked well and Australia had contributions across the board with four centurions and an attack that was all over Sri Lanka's struggling batting-order.
Lone quick Mitchell Starc built on his outstanding record in Sri Lanka, while Kuhnemann claimed a series-high 16 wickets at 17.18 to prove why he has been deemed so valuable in these conditions. He also showed plenty of grit to play through a sore thumb he injured in a BBL game on January 16.
After having little to do during the seam-dominated India-series, Lyon as expected shouldered plenty of responsibility and finished with 14 wickets at 22.5.
But this battle for the Warne-Muraliduran Trophy will be remembered for stand-in skipper Smith. He issued a reminder on his mastery in Asian conditions with brilliant back-to-back tons as his renaissance continues. Smith led superbly in the absence of Pat Cummins with his tactical nous coming to the fore as he made all the right moves in the field.
In contrast, Sri Lanka were bitterly disappointing in a sad end for retiring opener Dimuth Karunaratne as they slumped to their fourth straight Test defeat.