Chris Rushworth struck within the first ten minutes of the day trapping Sachithra Serasinge lbw for 26 followed by a wicket for Liam Plunkett the following over, who bowled Dimuth Karunaratne four short of his fifty leaving Sri Lanka A 192-6.
Two wickets fell in the 65th over with Scott Borthwick bowling Sachithra Senanayake on 48 followed by a run out by Mark Stoneman to dismiss Kosala Kulasekara (26).
Sri Lanka A were 278-9 once Ben Stokes caught Sajeewa Weerakoon off the bowling of Ruel Brathwaite the following over.
In the second over after lunch Mark Wood gets in on the action when Nilanka Prenaratne is caught by Gareth Breese at second slip for just 1.
Scott Borthwick and Mark Stoneman came to the crease with Durham requiring 220 to win but the former was trapped lbw by Kulasekara off the third delivery with Durham 1-1.
Durham were 30-2 in the eighth over after Stoneman was caught in the slips by Malinda Warnapura off Shaminda Eranga for 9.
Gordon Muchall (26) fell to the same fate in Eranga’s subsequent over which left Durham requiring another 187 to claim the win.
Michael Richardson was caught in the slips off Kulasekara for 7 which saw Ben Raine join Ben Stokes, who was dropped on 29, in the middle and by tea Durham were 78-4.
Raine was bowled by Senanayake for 7 in the first over after the break and his dismissal was followed by that of Breese who was bowled by Ernaga for 4.
Durham were 104-7, still requiring another 116 when Stokes was stumped off Senanayake for 51, having scored his fifty from 58 deliveries, including five fours and a six.
Liam Plunkett and Mark Wood put on a determined 114 run partnership which saw Plunkett reach his fifty from 64 deliveries which included four boundaries and a maximum.
As the pair chased down the runs required Wood was unfortunately run out on 48 which gave Rushworth the opportunity to come in to strike the winning boundary which claimed the win for the home side.