Chasing 263 for victory, Samarawickrama stood firm once again with a patient 91 off 107 balls to add to his century against Pakistan as the island nation wrapped up the contest in the 49th over.
The result moved Sri Lanka off the bottom of the standings and up to ninth, above Afghanistan thanks to a marginally better net run rate.
"I'm really happy to finish the game for my team, we needed a win, we haven't done well in the last three games," said Samarawickrama, who was named player of the match.
"When I went in the wicket wasn't easy... the fast bowlers bowled a good line and length. My plan was to bat deep and stick to the basics. I knew it would be hard in the latter stages."
The Netherlands had won the toss and opted to bat first but they had a poor start after Sri Lanka's fast bowlers Kasun Rajitha and Dilshan Madushanka ran through the top and middle order.
The European side were reeling at 91-6 when skipper Scott Edwards was sent back to the pavilion by Maheesh Theekshana, but Sybrand Engelbrecht (70) and Logan van Beek (59) rescued the Dutch side with a 130-run partnership.
The pair rotated strike and guided the team to a competitive total but they were bundled out for 262 in the final over of their innings as Rajitha and Madushanka finished with four wickets each.
"We didn't start well but we got ourselves to a pretty competitive total," Edwards said.
"Our batting hasn't quite clicked yet. It's obviously great that Sybrand and Logan chipped in with 130 runs. Ideally, we would get more runs at the top."
In response, Sri Lankan opener Pathum Nissanka laid the foundation for their chase with a knock of 54 that included nine boundaries but Aryan Dutt contained them with three wickets, dismissing Kusal Perera and Kusal Mendis cheaply.
But Samarawickrama built partnerships of 52, 77 and 76 with Nissanka, Charith Asalanka and Dhananjaya de Silva respectively to steady the ship before Dushan Hemantha came in and hit the winning runs.
The Dutch side, eighth, play Australia next on Wednesday while Sri Lanka play England a day later.
