It meant relief at last for the visitors on Wednesday as they finally gained a win after losing the Test match, three one-day internationals and the first two T20 games.
Afghanistan captain Ibrahim Zadran won the toss, and elected to bat first as they made 5-209 off their 20 overs.
Needing 19 to win in the last over, Kamindu Mendis hit Momand for two fours with the first and third deliveries, and was then lucky to escape a waist-high no-ball in the fourth which the umpire didn't call.
Needing 10 off the last two balls, Mendis failed to score off the second-to-last ball and then hit a six to fall three runs short.
Mendis remained unbeaten on 65 off 39 deliveries with two sixes and seven boundaries as Sri Lanka finished on 6-206.
Earlier, Afghanistan openers Hazratullah Zazai and Rahmanullah Gurbaz had got off to a brisk start scoring 72 runs in the first five powerplay overs without losing a wicket.
Zazai made 45 off 22 deliveries and Gurbaz, the player of the match, ended a lean patch by scoring 70 off 43 deliveries.
Spinner Akila Dananjaya and fast bowler Matheesha Pathirana took two wickets each for Sri Lanka.
Sri Lanka's opener Pathum Nissanka had to retire hurt on 60 because of an injury.
He and Kusal Mendis shared 64 for the first wicket but when Mendis was out for 23 and Kusal Perera went without scoring with the total on 65, Sri Lanka's momentum stalled.
After Nissanka left the field at 83, Sadeera Samarawickrama (23) and Kamindu Mendis shared 53 for the fourth wicket, bringing Sri Lanka back into the match.
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