Moeen Ali and Jack Leech took four wickets apiece as Sri Lanka were bowled out for 284 in their second innings after a strong last-wicket partnership and ended up losing the match by 42 runs.
England beat Sri Lanka by 42 runs in the third and final Test at the Sinhalese Sports Club in Colombo to complete a 3-0 whitewash.
Having set the hosts an improbable target of 327, England bowlers ran through the Sri Lankan top order on Day 3.
England had a first innings lead of 96 runs, made 230 all out in their second innings.
Legspinner Adil Rashid (5-49) and allrounder Ben Stokes (3-30) helped to bowl Sri Lanka out for 240 after the hosts went to tea on 183-2 at Sinhalese Sports Club.
Bairstow scored 110 off 186 balls, with nine fours and a six, in his first game since twisting his ankle while playing football almost a month ago during the ODI series against the Sri Lankans.
Making his return in the final Test of the series, a determined Jonny Bairstow struck up his 6th Test century to help England reach 312/7 at stumps on Day 1.
Broad will come in for pace spearhead James Anderson, while Bairstow will replace the injured Sam Curran and bat at number three.
England captain Joe Root was named man of the match for his magnificent 124 that helped England to a total of 346 in their second innings.
Sri Lanka were ruing their luck as only 17 minutes of play was possible after tea, but during that brief period, they let England back into the game.
Angelo Mathews struck up a gritty 88 to help the hosts reduce the deficit, however, the momentum is now with England as they close in on to win the 2nd Test and the series.
Joe Root's chanceless knock came as a big relief for England as he had accumulated only 52 runs in three innings in the series.
Akila Dananjaya grabbed six wickets but Root's century and Foakes's unbeaten fifty made sure England end Day 3 with a lead of 278.
Sri Lanka was all out for 336 in reply to England's 285, boosted to 290 with the penalty runs at Pallekele International Stadium.
Sri Lanka was all out for 336 in reply to England's 285, boosted to 290 with the penalty runs at Pallekele International Stadium.
The day belonged to Sam Curran, who helped England reach a competitive total with the spinners getting plenty of purchase on a dry surface.
Live Cricket Score, Sri Lanka vs England, 2nd Test, Day 1 at Pallekele: Follow all the updates from day one of the second Test between England and Sri Lanka at IndiaTV Sports.
Dananjaya was reported to the International Cricket Council by the match officials after the first Test, in which he took two wickets in 38.5 overs.
Chandimal strained his groin during the first Test in Galle which Sri Lanka lost by 211 runs inside four days on Friday.
After setting Sri Lanka an improbable winning target of 461 and two days to do it, England bossed the first test.
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