Zadran and Rahmat Shah (55) put on a 146-run stand for the second wicket to guide the visitors to 269-4 in the 47th over after they won the toss and chose to field first in Hambantota.
Earlier Charith Asalanka top-scored with 91 to help Sri Lanka reach a below-par 268 all out after a shaky start pushed them to 84-3 inside 20 overs.
The 21-year-old Zadran was dismissed by Kasun Rajitha, who was Sri Lanka’s most effective bowler on the day, and finished with 2-49 in his 10 over spell.
Zadran raced to his half-century in just 35 balls and hit 11 fours and two sixes in his innings.
Both his sixes came against rookie pacer Matheesha Pathirana, who recently made a name for himself with noteworthy performances for the latest IPL winners Chennai Super Kings.
Wayward Pathirana finished with 1-66 in 8.5 overs of his debut ODI.
Zadran and Shah anchored the Afghan innings after other opener Rahmanullah Gurbaz fell for 14 in the sixth over.
Mohammad Nabi (27) and Najibullah Zadran (7) remained unbeaten at the end to steer Afghanistan to victory.
Sri Lanka’s Lahiru Kumara took 1-21 in 4.3 overs as other Sri Lanka bowlers failed to make a dent.
Zadran said it was “very tough to get out” close to his fourth century and praised his bowlers for “a very good job” to restrict Sri Lanka below 300.
“I wanted to finish the game and get a hundred but that’s how it goes in cricket,” he said after the game.
“A target of 269 was a good score, but not that challenging. The ball was coming on to that bat and we just wanted to finish things off,” he added.
Earlier, a 99-run stand between Asalanka and Dhananjaya de Silva for the fifth wicket rescued the hosts. De Silva made 51 before being bowled by Nabi.
Left-arm seamer Fazalhaq Farooqi (2-58) claimed the wickets of Dimuth Karunaratne and Kusal Mendis in his opening spell, and then Fareed Ahmad and Mujeeb ur Rahman made further inroads.
After the dismissal of De Silva, captain Dasun Shanaka added 32 runs for the sixth wicket with Asalanka, but bowler Noor Ahmad accounted for the skipper with a well-disguised googly.
Dushan Hemantha backed up Asalanka well in a 48-run stand for the seventh wicket. He made 22.
Asalanka scored his 91 off 95 balls with 12 fours, before being run out in the last over.
Sri Lanka will use the series as preparation for World Cup qualifiers this month in Zimbabwe.
Afghanistan are already through to the sport’s showpiece event this year in India and will be testing their combinations.
(With AFP Inputs)
