James Taylor missed a maiden one-day century by 10 runs as England, electing to take first strike, scored 265 before they were all out off the last ball of their 50 overs in Colombo.
But Sangakkara's 90th one-day half-century laid the foundation that enabled Sri Lanka to pass the target in the day game at Premadasa stadium.
The left-hander put on 96 for the third wicket with fellow veteran Mahela Jayawardene (44) and 49 for the fourth with skipper Angelo Mathews.
England were left to rue bowling 12 wides in what eventually turned out to be a close game. Steven Finn, Chris Jordan and Joe Root sent down three each.
"It was a good, close game," said Mathews, who hit the winning boundary off Finn. "We had to fight hard. I was a bit nervous at the end, but I knew we had wickets in hand. It was a good team effort."
