New Zealand replied with 159 for four after bowling Sri Lanka out for 157 in Hamilton.
AS IT HAPPENED
The Black Caps won the ODI series 2-0, having also won both of the two Test matches. A three-match Twenty20 series between the teams starts Sunday.
The home win saw New Zealand top the Super League table in qualifying for the ODI World Cup in India this year.
Sri Lanka are ninth, outside the top eight who automatically go to the World Cup, and now face a qualifying tournament in Zimbabwe starting in June.
Young’s 86 runs off 113 balls dug New Zealand out of trouble, Sri Lanka’s seamers having made life hard for the hosts early on.
His fifth-wicket partnership of 100 runs with Henry Nicholls sealed the result for New Zealand.
“We were one down when I came in. It was a bit more nerve-racking later on when we were three or four down,” said man-of-the-match Young.
“One of the good things about this team is that we can bat a long way down, so I had full confidence that we would get the job done.
“It was nice to be out there at the end and knock off the runs,” he said.
New Zealand made a terrible start after they were set a target of 158.
Openers Chad Bowes and Tom Blundell were both caught behind off Lahiru Kumara’s bowling to leave the Black Caps on 6-2.
Sri Lanka wicketkeeper Kusal Mendis then took his third straight catch when Daryl Mitchell got a faint touch on Kasun Rajitha’s delivery.
Black Caps captain Tom Latham briefly halted Sri Lanka’s momentum in a partnership of 38 with Young, only to be clean bowled by Dasun Shanaka for eight.
New Zealand were in trouble at 59-4 before Nicholls came to the crease to help put the game beyond Sri Lanka.
Nicholls finished on 44 not out, sealing the win by clubbing a four to the boundary after providing crucial support for Young.
It was another frustrating display by Sri Lanka, who were skittled for just 76 in a 198-run defeat in the first ODI on Saturday before the second game on Tuesday was washed out.
Sri Lanka won the toss but lost three wickets in the first 10 overs as top-order batters Kusal Mendis and Angelo Mathews both went for ducks.
Sri Lanka were wobbling at 4-49 when Henry Shipley caught Charith Asalanka off Mitchell’s bowling.
The Black Caps seamers kept the tourists under pressure as Matt Henry, Mitchell and Shipley all took three wickets each.
Opening bat Pathum Nissanka top-scored with 57, managing partnerships of 31 and 30 with Asalanka and Dasun Shanaka respectively as Sri Lanka reached 100-6 before the opener was run out.
Shanaka, their captain, tried to rally his side by hitting two huge sixes before he went on 31 off 36 balls.
Sri Lanka were in deep trouble at 133 for eight before New Zealand polished off the tail.