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.
Kusal Mendis' battling half-century salvaged a difficult day one for Sri Lanka as they reached 229/9 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.
Gus Atkinson scored a superb maiden century as England's lower order collected quick runs against a ragged Sri Lanka bowling attack to post 427
England captain Ollie Pope returned to form with a classy unbeaten 103 to guide his team to 221/3 on a weather-affected first day of the third and final Test.
Sri Lanka used the seamer friendly conditions at Kingsmead to reduce South Africa to 80/4 before rain stopped play on the opening day of the first Test
Sri Lanka were dealt another injury blow at the World Cup with seamer Lahiru Kumara ruled out of the rest of the tournament due to a left thigh muscle injury.
Spinner Keshav Maharaj took five wickets as South Africa secured a 109-run victory over Sri Lanka on the last day of the second Test.
Seamer Dane Paterson took a career-best 5-71 and Temba Bavuma was unbeaten on 48 as South Africa closed the third day
South Africa were five wickets from victory as Sri Lanka finished the third day of the first Test on 103-5 in their second innings after being set a 516-run target on Friday.
Ryan Rickelton scored a maiden Test century as the hosts finished on 269-7 against Sri Lanka on the opening day
IMAGES from Day 1 of the second Test between England and Sri Lanka, at Lord's, on Thursday.
Nissanka had featured in a 41-run opening partnership with Dimuth Karunaratne, who scored 20 before being undone by a rising delivery from Kagiso Rabada that forced an edge behind to wicketkeeper Kyle Verreynne.
Dasun Shanaka on Saturday said someone had to 'chip in' with the side's frontline bowlers out with injuries.
IMAGES from the third Test played between England and Sri Lanka at the Oval on Sunday
Sri Lanka, who won the T20 World Cup in 2014, have two warm-up games in Melbourne before they begin their World Cup campaign with a qualifying match against Namibia on October 16.
India opener Ishan Kishan was admitted to a city hospital and underwent a brain scan after being struck on the head during the second T20I against Sri Lanka, in Dharamsala, on Saturday.
Injury-hit Sri Lanka and South Africa seek winning start to World Cup
IMAGES from Day 4 of the 2nd Test between England and Sri Lanka, at Lord's, on Sunday.
'Pathum Nissanka is easily one of the best batters to have come out of Sri Lanka in the recent past and he has delivered once again,' he tweeted with an applause emoji.
IMAGES from the World Cup match between England and Sri Lanka, at the M Chinnaswamy Stadium in Bengaluru, on Thursday.
Both players accepted the proposed sanctions, the ICC said.
Binura Fernando, Pramod Madushan, Dushan Hemantha back in Sri Lanka squad
Sri Lanka have called up leg-spinning all-rounder Dushan Hemantha, while Chamika Karunaratne will be the travelling reserve player.
Bangladesh handed Sri Lanka a crushing seven-wicket defeat in their first warm-up match of the ICC ODI World Cup, in Guwahati on Friday to make a winning start.
India beat Sri Lanka by seven wickets in the second Twenty20 International to take an unassailable 2-0 lead
Images from the first Twenty20 International between India and Sri Lanka, in Lucknow, on Thursday.
Sri Lanka have been hit hard by injuries to key players in the run up to the ongoing Asia Cup.
Royal Challengers Bangalore announced that Sri Lankan duo of Wanindu Hasaranga and Dushmantha Chameera have been released from the team's bio bubble ahead of the IPL Eliminator match against Kolkata Knight Riders on Monday.
Hosts New Zealand were in trouble as Sri Lanka reduced the Kiwis to 165 for five on day two of the first Test.
Images from the third and final ODI between India and Sri Lanka at the Greenfield International Stadium, in Thiruvananthapuram, on Sunday.
After playing a major role in Chennai Super Kings' IPL triumph, young pace bowler Matheesha Pathirana will be hoping to make the same impact for Sri Lanka in the ODI series against Afghanistan.
Ahead of the ICC Men's ODI World Cup 2023, here's a full list of the final squads of all ten teams.
Sri Lanka Cricket picked a 20-member squad for the white-ball series starting on January 3.
Lanka's entry into the 2023 World Cup is marked with injuries, modest form of players and rumours of the team getting a new captain that was put to rest at the last minute.
The Netherlands will have a spring in their stride when they take on a struggling Sri Lanka on Saturday.
Images from the second One-Day International at the Eden Gardens in Kolkata on Thursday.
Their house in complete disarray after consecutive defeats, Australia will look to wake up from the slumber and return to winning ways against an equally stuttering Sri Lanka in the World Cup match in Lucknow on Monday.
Pakistan are traditionally good against spinners but Babar Azam and Co. would take the likes of promising Dunith Wellalage and company lightly at their peril.
Images from the T20 World Cup match between Sri Lanka and Ireland, in Hobart, on Sunday.
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