In a match reduced to 38 overs a side by early morning rain, Durham were put in to bat by Essex and fell to 30-3.
But former England captain Stokes hit 43 off 27 balls, hitting five fours and two sixes, before Colin Ackermann added an unbeaten 80 that helped them post 229-5.
Essex opener Noah Thain made 76 but the visitors lost the rest of their top order cheaply, and were bowled out for 209.
Gay sat out the match as a precaution after retiring hurt in Friday's loss to Middlesex.
Elsewhere, Jake Libby's fourth century in as many One-Day Cup outings was not enough for Worcestershire as Glamorgan snatched a two-wicket victory off the last ball at Cardiff.
Libby extended his outstanding run as the Worcestershire skipper made 105 off 114 balls in his side's 278-9.
Glamorgan were quickly reduced to 46-3 in reply but Callum Rhys Nicholls (70) and Jack Hope-Bell (58) reversed the trend and captain Andy Gorvin found the boundary from the last ball of the game to snatch the win.
Group B leaders Middlesex eased to an 87-run win over Derbyshire on the back of a 156-run third-wicket partnership between Max Holden (65) and Ben Geddes (109).
Hampshire openers Ali Orr (105) and Ben Mayes (109) put on 225 for the first wicket in their 51-run win over Sussex.
A superb unbeaten 133 from Daniel Bell-Drummond powered Kent to a six-wicket win over Group A leaders Leicestershire to keep their hopes of progress alive.
Nottinghamshire could not take advantage of Leicestershire's loss as Gloucestershire beat them by four wickets with five balls remaining at Cheltenham despite captain Haseeb Hameed's 85.
Luke Procter also made 85 as Northamptonshire secured a seven-wicket victory over Somerset at Wantage Road while Warwickshire secured a two-wicket win over Lancashire.
