The North Division leaders benefited from being asked to bat first as they made 162 for eight then, in rapidly fading light, Yorkshire limped to 49 for five before rain ended play after 10 overs.
Yorkshire will now have to win both their remaining group games, at home to Leicestershire on Thursday and at Trent Bridge on Friday, to have any chance of reaching the last eight.
The visitors were without Michael Vaughan after the England selectors requested that he should be rested, but he would not have fancied facing Steve Harmison in the gloom as the paceman took the last two wickets to fall.
The competition’s leading run-scorer, Anthony McGrath, had already gone for eight, driving Liam Plunkett to extra cover as the pressure mounted.
Wicketkeeper Gerard Brophy’s five victims for Yorkshire counted for little when he walked across his stumps and was bowled by Shaun Pollock in the third over to leave Yorkshire on nine for two.
He had already declined first-time opener Adil Rashid’s call for a second run and seen him stranded without facing a ball.
Phil Mustard launched Durham’s innings with 49 off 37 balls, including two sixes. For the third successive innings he fell in the 40s when he skied Richard Pyrah to Brophy.
Dale Benkenstein picked up Darren Gough for six as 16 came off the Yorkshire captain’s first over. But the Durham skipper departed for 29 off 17 balls when he lifted Pyrah’s slower ball to long-on.
After taking Yorkshire’s best Twenty20 figures of 4-20 in Sunday’s tied match between these teams, Pyrah finished with 3-32 to take his tally to 14 in this season’s competition.
Gough tightened up superbly in his last three overs to finish with 2-28, but was left to rue his decision to field first.