Jemimah Rodrigues’s magnificent unbeaten 112 from 58 balls guided Yorkshire to victory, secured off the final ball by Linsey Smith.
But the Diamonds knew only a bonus-point victory would keep their chances alive. To secure that, they needed to chase 185 inside 16 overs.
Despite Rodrigues’s efforts, Susie Bates’s 47 and a rapid 42 from Danni Wyatt helped Vipers to a total that was only chased down from the final ball.
Vipers will face Loughborough Lightning in the semi-final for the chance to take on Western Storm.
Yorkshire lost their openers inside the powerplay at the start of their chase – both to Tash Farrant – as Lauren Winfield departed for a second-ball duck and Alyssa Healy was caught for 22.
India star Rodrigues was aggressive from the outset, hitting eight boundaries in her first 20 balls to reach 42.
Her half-century came from 26 deliveries and her partnership with Hollie Armitage stretched to 90 from 54 balls to take Yorkshire to 118-2 in the 13th over.
But the Diamonds quickly fell to 121-5. Amanda-Jade Wellington trapped Armitage for 23 and also dismissed Bess Heath two balls later for a duck, before Fi Morris had Alice Davidson-Richards caught behind.
As the 16th over ticked by, Yorkshire’s hopes ended. But Rodrigues was undeterred, striking cleanly to all parts of the ground.
She guided Yorkshire to within striking distance, needing 17 from 12 balls. Her century came from 51 balls and included 16 fours and one six. There were 10 runs needed from the final over, with Smith’s single off the final ball clinching victory.
Winfield said: “Great performance, I think they probably got 20 or 30 more than they should have done, certainly more than we would have liked but we know it is a really good wicket here.
“Jemimah Rodrigues was unbelievable. She has just got better and better this competition. The last three, four, five games she has really grown into the role and hit her straps. That was as good as I’ve seen. For her age she has an unbelievable head on her shoulders. She is just keen to learn.
“She is always asking questions. She has a fantastic cricket brain and all the shots, very exciting and glad she is on our team.
“We have seen her perform well in a couple of tight chases and been a bit of a finisher for us. We are all nervous as hell on the sidelines and she looks cool as a cucumber. It was an unbelievable knock.”