Surrey’s pace bowlers Dan Worrall (2-14) and Reece Topley (2-20) made early inroads into Durham’s top order as they struggled to put runs on the board.
When Sam Curran’s quick-thinking and expert arm ran out Colin Ackermann at the non-striker’s end to leave Durham 61-5 at the halfway stage, the visitors looked to be in big trouble.
But the lower order fired and De Leede (24) and Raine (23) added quickfire boundaries, along with Jones’ powerful striking, to give Durham something to defend.
Their own pace bowlers restricted Surrey early on in their reply, with Brydon Carse picking up the wickets of England’s Will Jacks and Laurie Evans, before Rory Burns, batting at four, also departed cheaply.
But Sibley stayed put and it was his partnership with Curran which took the game away from Durham.
They both departed before the end, Sibley to the spin of Callum Parkinson and Curran to Raine, but they had already done the job when Jamie Overton came in to hit the winning runs.