On a dusty wicket tipped to soon become very tricky for the batters, Smith (120no from 239 balls) and Carey (139no from 156) forged a match-defining 239-run stand that ripped momentum back in Australia's favour.
Australia (3-330) went to stumps 73 runs ahead of Sri Lanka, having passed the hosts' first-innings 257 around an hour before stumps.
Stand-in captain Smith sparked the fightback, coming in when the tourists were in serious trouble at 2-37 and continuing a brilliant resurgence with the bat.
Smith had struggled as an opener to finish the previous home summer and wobbled to begin the most recent one, but now has four tons from his past five Tests.
That includes two centuries from as many innings in the two-match Sri Lanka series.
It was vintage Smith this time, the straight-laced skipper bringing out his favourite cover drive and even trying his hand at the reverse sweep for one four off Ramesh Mendis (0-70).
It was easy to forget the pitch in Galle was supposed to be difficult for the batters, such was Smith's ability to split the fielders and find the boundary.
He brought up his 36th Test century hitting right-arm finger-spinner Ramesh for four past mid-wicket as shadows began falling on the ground around 4pm.
From the fans on top of Galle Fort, to the Sri Lankan fielders themselves, everyone clapped for Australia's subcontinent master.
Just after lunch, Smith had passed Ricky Ponting to become Australia's most prolific run-scorer in Asia with 1,983 runs and counting.
He has now scored seven Test centuries in Asia, passing Allan Border (six) to set a new record for Australian batters.
On any other day, Carey would have stolen the show after being shifted up to No.5 for the first time in his Test career and playing a chanceless innings.
Josh Inglis' earlier absence from the field with back soreness forced Australia to shift him down the order, with Carey the man pushed up and out of his comfort zone.
But coach Andrew McDonald would be forgiven for keeping the affable wicketkeeper up higher after he passed his previous Test-high score of 111.
Carey reiterated his status as one of Australia's leading proponents of the sweep shot, and Ramesh proved a favourite victim during his rapid-fire innings.
He popped the finger-spinner's full toss past fine leg with a reverse lap shot for four at one stage, and lifted him over mid-on for six midway through the second session.
Carey brought up his second Test century sweeping a struggling Prabath Jayasuriya (1-107) between the fielders for a four past square leg.
The knock will have silenced any suggestions recent debutant Inglis could be coming for Carey's job as wicketkeeper.
Sri Lanka had made a positive start pushing Australia to 2-37 early on, with out-of-sorts Marnus Labuschagne (4) again missing out as part of the early carnage.
With the pitch expected to break up, the home side must have felt ready to rip through the Australian middle-order when Nishan Peiris (2-70) trapped opener Usman Khawaja (36) lbw 15 minutes after lunch.
But Sri Lanka simply had no answers to Smith and Carey, and almost appeared to give up on setting attacking fields when it became clear the duo would chase their lead down.
Smith had a couple of wobbles in the second session, challenging the decision when given out lbw on 23, and missing a turning Peiris delivery that bounced just above the stumps.
But those were the only times Sri Lanka came close to taking either his or Carey's wicket.
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