England wasted no time wrapping up a fine win in Galle, with Jonny
Bairstow and Dan Lawrence requiring just 36 minutes to knock off the 36 runs required for victory.
This was Joe Root's team's fourth overseas win in succession — the first time they have achieved that since 1957 — and represents a fine start to an epic year that sees them face India home and away, world No1 side New Zealand at home, then contest the Ashes in Australia.
England had minimal preparation, had seven players unavailable for one reason or another and lost the toss.
"Any Test win, you've got to take a lot of confidence from and a lot of heart from the way that we've gone about this game," said Root. "If we keep learning from this game, from the good things and also the mistakes that we've made, we will also get better and will be very hard to beat.
"It's really important that we started off strong this winter and really pleasing in the manner that we have done it.
"Look back a couple of years and our record away from home was very poor. We aren't the finished article, we've got a long way to go, we are making little errors here and there, but we are getting better — and that's seen by the results we are having. There will be bigger challenges throughout the winter and beyond, but we are going in the right direction and we can't ask any more from the players in that respect."
Poor Sri Lankan batting on the first day saw them bowled out for 135, then Root's fourth Test double-century saw England rack up a lead of 286. Sri Lanka were much improved in the second innings, with their 359 setting England 74 to win.
A disastrous start last night saw England lose their openers to Lasith Embuldeniya, then Root run out in shambolic fashion. But Bairstow, back after 13 months out of the side, and debutant Lawrence had shared 24 by stumps and calmly completed the task this morning.
"With those run chases, they are always very tricky and a little bit nervy because of the expectation," added Root. "You want to just get off to a very strong start. Unfortunately, we weren't able to do that, and it was always just going to take one partnership, two guys just grabbing it by the scruff of the neck and showing some maturity and calmness out there. It was a bit hairy for a period, but for Dan to go out and play in that manner is really impressive."
There were few alarms as the pair averted risk in taking England home, although Sri Lanka wasted a review on a Lawrence lbw shout, then failed to send another upstairs an over later that would have been out.
The pair ran hard for their singles and the Bairstow sweep that took England to victory was just the second boundary in their stand of 62.
"On a pitch like that, if you're not looking to score, then there will be a ball that comes your way," said Bairstow. "That was the mindset: to go out and be busy."
Root was certain Sri Lanka would continue their improve in Friday's Second (and final) Test.
Sri Lanka coach Mickey Arthur said it was "unlikely" that his team would have their captain Dimuth Karunaratne back from a thumb injury by then, but seamers Suranga Lakmal and Lahiru Kamara will be available.
Root was pleased England's bowlers have an extra day of recovery, but changes to the attack are likely. Jimmy Anderson, Chris Woakes and Olly Stone are among the seamers in contention, while Root said spinner Moeen Ali's situation will be taken "day by day".
Moeen tested positive for Covid-19 on arrival in Sri Lanka and was only released from quarantine on Saturday. Root said it "would be wrong to completely rule him out", but with four
Tests in India to come, England will be cautious in their approach.