Hasaranga nearly pulled off the win with 59 off 52 balls before perishing in the penultimate over as Pakistan hung on to restrict the visitors to 293-9.
Salman Ali Agha’s unbeaten 105 off 87 balls had earlier propelled Pakistan to 299-5 after Hasaranga's three-wicket burst had left the home team struggling at 95-4 in the 24th over.
The victory extended Pakistan’s ODI momentum under new captain Shaheen Shah Afridi after a 2-1 series win over South Africa last week.
Pakistan fast bowlers found it tough to control the wet ball because of heavy dew at the Pindi Cricket Stadium as Sri Lanka openers — debutant Kamil Mishara (38) and Pathum Nissanka (29) — provided a rollicking start of 85 off 70 balls.
But fast bowler Haris Rauf (4-61) picked up three quick wickets when he had Mishara caught at mid-on and the next ball Kusal Mendis played the pacer back onto his stumps.
Sri Lanka slipped to 90-3 in Rauf’s next over when he found the outside edge of Nissanka before Sadeera Samarawickrama (39) and captain Charith Asalanka (32) put the chase back on track with a 57-run stand as Afridi kept the pacers going with the wet ball.
Rauf then returned and broke the threatening stand in the 27th over when Babar Azam plucked a superb one-handed catch in the first slip to dismiss Samarawickrama, and left-arm spinner Mohammad Nawaz had Asalanka stumped in the 32nd over with Sri Lanka still needing 107 for victory.
Hasaranga, who walked in the 34th over, dug in with the tailenders and completed his half-century off 45 balls before he holed out to long-on while going for a big hit against Naseem Shah in the 49th over.
