Walking out with intent and flair, the wicketkeeper-batter smashed a quickfire 51 off just 56 deliveries in the morning session, propelling England to a strong 387.
Spinner Prabath Jayasuriya led the charge with a five-wicket haul as Bangladesh collapsed for just 133 in their second innings, handing Sri Lanka a win by an innings and 78 runs.
The result was the first drawn game in Galle for 12 years.
Sri Lanka are still 518 runs behind and will need a Herculean effort to avoid the follow-on even though more rain is forecast for Saturday.
Spin twins Matthew Kuhnemann and Nathan Lyon combined to dismantle Sri Lanka and bowl Australia to a crushing victory by an innings and 242 runs in the opening Test in Galle on Saturday.
Dinesh Chandimal smashed a maiden double hundred and Prabath Jayasuriya claimed 12 wickets in a dream debut to script Sri Lanka's series-levelling victory by an innings and 39 runs in the second Test against Australia in Galle on Monday.
Dinesh Chandimal smashed 118 not out and Kamindu Mendis produced a half-century in his debut Test to help Sri Lanka eclipse Australia's first innings 364 on day three of the second Test in Galle on Sunday.
Dinesh Chandimal smashed his second half-century of the match to put Sri Lanka in the box seat in the opening Test against Pakistan in Galle on Monday.
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.
Victory for South Africa followed Test success over West Indies in Guyana in August and Bangladesh in a two-Test series in October.
Angelo Mathews, playing his 100th Test, batted aggressively and got a reprieve when Babar floored a sitter at cover when the batsman was on 36.
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.
Sri Lanka put themselves in a good position on the third day of the opening Test against New Zealand after Dimuth Karunaratne and Dinesh Chandimal made half-centuries but the hosts lost some of their momentum to reach 237-4 at stumps in Galle on Friday.
Dimuth Karunaratne's Test career ended in a whimper as Sri Lanka's most prolific Test opener fell caught behind to Kuhnemann after making 14.
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.
Steve Smith became the 15th member of Test cricket's 10,000-run club as he and opener Usman Khawaja smashed hundreds to help Australia rack up 330/2 on the opening day of the first Test against Sri Lanka.
Sri Lankan batter Dimuth Karunaratne is set to retire from international cricket after playing his 100th Test -- the second and final Test against Australia, starting in Galle on Thursday.
Sri Lanka's decision to bat first backfired when they were all out for 236 on Day 1 of the first Test.
IMAGES from the Day 4 of the 1st Test between England and Sri Lanka in Manchester on Saturday
Kamindu Mendis maintained his red-hot form and struck a majestic 114 to power Sri Lanka to 302/7 on the opening day of the first Test.
South Africa require five wickets and Sri Lanka need 143 runs as the second Test heads for a potentially exciting conclusion
Jamie Smith's maiden Test century helped England take a 122-run lead on Day 3 in the first Test against Sri Lanka
Dinesh Chandimal, Sri Lanka's T20 international skipper and has rejected offers to play in the sixth edition of the IPL, cricket board sources claimed.
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.
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.
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
Sri Lanka skipper Dinesh Chandimal, on Thursday, appealed against the ICC's decision to suspend him from the third Test of the ongoing tour of the West Indies due to ball-tampering.
Sri Lanka wicketkeeper-batsman Dinesh Chandimal has undergone surgery after injuring his thumb during a domestic match last week.
New Zealand captain Tim Southee said playing two Tests at Galle, known as a spinner's paradise, was always going to be challenging.
With Sri Lanka's cricket team performing better under Sanath Jayasuriya, he is all set to get a contract extension.
Sri Lanka Test captain Dinesh Chandimal was withdrawn on Monday from the 16-member squad for the Asia Cup because of an injury during a recent domestic tournament. The 28-year-old batsman injured a finger during a domestic Twenty20 match and needed more time to recover, Sri Lanka Cricket (SLC) said.
Steven Smith and Shaun Marsh scored unbeaten half-centuries to launch a strong response from Australia after Dinesh Chandimal's patient hundred pushed Sri Lanka's first-innings total to 355 on the second day of the third and final Test on Sunday.
Sri Lanka captain Dinesh Chandimal will miss the third and final Test against the West Indies after his appeal against a ball-tampering ban was dismissed by a judicial commissioner.
South Africa bowled poorly in the first hour, but still managed to reduce the visitors to 54 for three as Sri Lanka gave their wickets away with injudicious stroke-play.
The same charge was levelled against Australia batsman Cameron Bancroft who was caught on camera rubbing a piece of sandpaper on the ball against South Africa in March.
Dinesh Chandimal made 147 not out and Angelo Mathews ended his century drought to help Sri Lanka rediscover their competitive edge against India on day three of the third and final Test.
At a loss to explain Sri Lanka's dismal performance against India, skipper Dinesh Chandimal on Monday said the 0-3 thrashing was the 'worst' Test series of his career and his team has no excuses to offer.
Sri Lanka captain Dinesh Chandimal has been suspended from his team's upcoming two games in the Nidahas T20 Trophy
Sri Lanka batsman Dinesh Chandimal has been ruled out of the remaining two matches in the One-Day International series against India after fracturing his thumb in the third ODI.