|Second Test, Pallekele (day five)|
|England 290 (Curran 64, Perera 4-61) & 346 (Root 124, Foakes 65*, Akila 6-115)|
|Sri Lanka 336 (Silva 85) & 243 (Mathews 88, Leach 5-83, Moeen 4-72)|
|England won by 57 runs|
England claimed their first series win in Sri Lanka since 2001 with a 57-run victory in the second Test.
The hosts started day five in Pallekele on 226-7, needing 75 more, and calmly added 14 in 28 balls.
But Moeen Ali drew Niroshan Dickwella into edging to first slip for 35, before bowling captain Suranga Lakmal two balls later for a duck.
Jack Leach removed Malinda Pushpakumara to bowl Sri Lanka out for 243 and claim his maiden Test five-wicket haul.
England lead the three-match series 2-0, with the final Test in Colombo starting at 04:30 GMT on Friday.
Regardless of the result of that game, England will climb above South Africa into second in the International Cricket Council rankings.
This was England's first away series win since beating South Africa in 2016 and their first series victory away from home under captain Joe Root.
Spinners took 38 wickets in the match, a record in Test cricket.
- Root wants England to be 'trendsetters'
- England's attacking approach pays off - Agnew
- TMS podcast: Vaughan & Agnew review England's series win
England hold their nerve
History suggested England were favourites to wrap up victory on day five, with only four teams since World War One having scored 65 or more runs with three wickets left to win a Test.
There was still plenty of trepidation among England fans that Sri Lanka could reach their target of 301, not least with the irrepressible Dickwella at the crease and capable of scoring quickly.
And when he largely shelved his attacking instincts to comfortably tap singles with Akila Dananjaya, it felt like the Test was heading for a tight and thrilling finish.
But Moeen showed skill and guile to lure Dickwella into a flashy drive, giving a full delivery more flight and dip before it turned to take the edge as Ben Stokes claimed the catch.
Moeen's second was even better - a dream dismissal for an off-spinner - angling the ball towards slip from around the wicket and finding sharp turn to bowl Lakmal through the gate.
A magnificent Test ended in slightly anticlimactic fashion as England waited for the third umpire to confirm that Pushpakumara had not hit the ball into the ground in chipping it back to Leach, who finished with 5-83.
Barren run ends as Root era begins
Between the 2-1 victory in 2001 and this win, England have played three Test series in Sri Lanka, losing 1-0 in 2003-04 and 2007-08 and drawing 1-1 in 2011-12.
This Sri Lanka side may be shorn of former greats who played in those series, but they did beat South Africa 2-0 in July and this remains a tough place to play.
The result is also impressive given England's dire struggles over the past two winters - a 4-0 Ashes defeat followed by losing in New Zealand this year and a 4-0 thrashing by India after a draw with Bangladesh under Root's predecessor Alastair Cook the previous year.
England's spinners lacked control at times but outperformed their Sri Lanka counterparts, with Leach, Moeen, Adil Rashid and Root taking 19 wickets in the Test, the other coming from a Stokes run-out.
It is only the third time in England's 363 Test victories they have won without a seamer taking a wicket, with Sam Curran and James Anderson hardly used on a turning pitch but both contributing vital lower-order runs in the first innings.
This Test could prove the moment England become Root's side outright. He talked before the series about wanting to be more "courageous" on subcontinental pitches and his team bought into it here.
They batted positively, mostly with calculated risk among some more rash shots, to put the pressure back on Sri Lanka's bowlers, while Root largely marshalled his spinners well and played the most decisive innings of the game with a sublime 124 on day three.
This is also the first time an England side have won all three series in all formats on tour, albeit they only played Sri Lanka in a one-off Twenty20.
'A fantastic effort' - reaction & analysis
England head coach Trevor Bayliss on Sky Sports: "It is only England's second series win here. Coming here, playing a team in their home conditions - conditions that are foreign to us - it is a fantastic effort.
"The spinners were a bit below par in the first innings; we didn't get quite enough balls in the right areas. We spoke about that and, under pressure to perform in the second innings, they did a fantastic job.
"Both Rory Burns and Ben Foakes were playing in their second Tests but looked so calm. When they are batting it looks like they are playing in their 30th or 40th Test. That is a great sign going forward. That sends a message to the opposition. We knew Foakes was a very good keeper and he has proved it in this match."
Ex-England captain Michael Vaughan on The Cricket Social: "They've won the key moments, the moments that matter, which is exactly what you need to do in Test match cricket.
"I don't remember seeing an England team with as much talent and that's why it's frustrating when we have performances like at Trent Bridge and at Lord's against Pakistan."
England slow left-armer Jack Leach: "Unbelievable! It's a great feeling. These boys (Moeen and Adil Rashid) have helped me out so much. It was good to play on this wicket but, at other times, I felt it was tough."
England leg-spinner Adil Rashid: "It feels good to have three spinners in the team. We all know our roles and help each other out. It's nice to make history and hopefully we can carry that on now."
Sri Lanka captain Suranga Lakmal: "Both sides played very good cricket. It's been a good five days and a very challenging wicket."