Off-spinner Nishan Peiris picked up a six-wicket haul on debut as Sri Lanka crushed New Zealand by an innings and 154 runs.
Australia, who have already secured their place in the final of the World Test Championship against South Africa, won the opening Test, also in Galle, by an innings and 242 runs.
Sri Lanka left-arm spinner Prabath Jayasuriya wreaked havoc with the ball to leave New Zealand on verge of a big defeat in the second Test.
Smith's unbeaten 120 is his second successive hundred of the series while Carey made a career-best 139 not out hitting 22 fours and three sixes between them.
Australia's Usman Khawaja struck a maiden double hundred and Josh Inglis got a century on his Test debut against Sri Lanka to power the tourists to a mammoth 654/6.
It remains to be seen if the right-arm spinner will be available for SRH's home fixture against Chennai Super Kings on April 5.
Nic Pothas appointed as interim coach of Windies
Azharuddin, whose nomination was rejected two years ago, submitted his papers to former Chief Election Commissioner VS Sampath on Wednesday.
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