England thrashed the tourists by an innings and 88 runs inside three days to win the first Test at Headingley on Saturday and so go 1-0 up in the three-match series.
James Anderson made the most of overcast conditions ideally suited for swing bowling with a match haul of 10 for 45.
In the process, he became the first England player to take 10 wickets in a Test at Headingley since fast-bowling great Fred Trueman did so on his Yorkshire home ground against Australia back in 1961.
The wicket-keeper's knock was the cornerstone of England's 298, with Sri Lanka then shot out for 91 and 119 as man-of-the-match Bairstow, also enjoying himself behind the stumps, held nine catches.
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Bairstow has been in fine form for both Yorkshire and England recently, with his Headingley hundred following his maiden Test ton, an unbeaten 150 against South Africa at Cape Town in January.
"The bowlers, you don't want to take it for granted -- but you knew with those two (Anderson and Stuart Broad), the skill they have got, it would be really hard work for Sri Lanka."
Bairstow, son of late David Bairstow, himself a Yorkshire and England wicket-keeper, has had a stop-start international career since making his limited overs debut in 2011.
But he has looked increasingly assured as an England player since he made a match and series-clinching 83 not out in a one-day international against New Zealand at Durham's Chester-le-Street headquarters -- the venue for next week's second Test -- in June last year.
"I remember the first time I saw him play, at Scarborough, he played differently to everyone else -- we couldn't stop him scoring.
One downside for England is that Ben Stokes could be
ruled out of the second Test at his Durham home ground with a knee injury he suffered at Headingley.
England are due to give up an update on the all-rounder's fitness, and name a squad for the second Test, after he has had a scan on Sunday.
England's problems are as nothing, however, compared to those of Sri Lanka, who must somehow find a way to make runs if they are to avoid a repeat of their Headingley debacle.
"It was quite an embarrassing defeat ... Humiliating," said Sri Lanka captain Angelo Mathews after his side were dismissed twice inside 72 overs in Leeds.
"Anderson showed his class, and Stuart Broad was brilliant as well," he added.
"You have to be realistic, batting against these guys in these conditions.