Dasun Shanaka the only batter to pass 20 in another below-par display.
David Willey took 4 for 64 as England cruise home with seven overs to spare to take unassailable 2-0 lead.
Mendis, Hasaranga and Chameera show spirit but lack support in five-wicket loss.
alan and Bairstow contribute with fifties; Chameera career-best 4 for 17 was the only bright spot for the visitors in the third T20I.
The hosts clinched the series with a five-wicket win in the 2nd T20I.
Sri Lanka never really got to grips with the variation and control of the England attack
David Willey have been picked for T20I squad for the three-match series against Sri Lanka starting on June 23.
Sri Lanka have announced a 24-member squad for the limited-overs tour against England, starting 18 June.
England men will start their home summer with two Tests against world's number one side New Zealand.