Yorkshire ended their Group B campaign at the Champions League Twenty20 without a win after going down by four wickets in their final match against Chennai Super Kings.
Gary Ballance slammed five sixes in his 58 to get Yorkshire up to 140-6 but Chennai, who were also already eliminated, chased down their target in the penultimate over.
Yorkshire, sent in to bat in Durban, recovered from 43-3 thanks to a fourth-wicket stand of 78 between David Miller and Ballance.
Miller's 28 came off 26 deliveries but was overshadowed by his partner's 38-ball contribution.
Ballance hit two maximums in an over off Chennai captain Mahendra Singh Dhoni (0-25) - giving himself a rare outing with the ball - and Ben Hilfenhaus (1-32) before being run out at the start of the final over.
Yorkshire seamers Oliver Hannon-Dalby (2-23) and Steven Patterson (2-22) each struck an early blow to leave Chennai on 26-2 in the fifth over of their pursuit.
But Suresh Raina (31), Subramaniam Badrinath (47) and Dhoni (31) steered the Indian Premier League side over the line with six balls to spare.
The result completed a disappointing tournament for both teams. Chennai finished in third place in Group B with eight points, while Yorkshire's two points came from a rain-off.