Defending a total of 148-7, the Outlaws seemed certain to be on the wrong end of the result as the visitors coasted to 99-2.
Harry Gurney, with 2-29, including a crucial wicket in the final over, de-railed the run-chase, with Luke Fletcher taking 2-31 and ending the Vikings’ chances of reaching the quarter-finals.
Yorkshire had required 12 from the final six balls but fell short on 145-7, leaving Notts victors by three runs.
Earlier, Adam Lyth returned the best figures of his career as the Vikings struggled to keep their qualification hopes alive.
The 31-year old, who took three wickets against Durham on Friday evening, bettered all of his previous efforts to finish with 5-31.
Notts won the toss and opted to bat first but soon ran into trouble. Joe Clarke top-scored, falling for 50, one delivery after reaching his half-century.
Clarke faced 46 deliveries and hit three fours and two sixes, putting on 66 with Jake Libby, who made 35. Dan Christian plundered an unbeaten 31 from only 16 balls.
Lyth looked to cement a fine individual performance by steering his side to victory but fell for 48, heralding the start of a dramatic collapse.
The early stages of the afternoon featured contrasting moments for Keshav Maharaj, Yorkshire’s South African international. In only the second over he spilled Clarke, on three at the time. With his fingers still stinging Maharaj then made his mark on the day by clinging on to a sharp offering to dismiss Alex Hales for only seven, off Tim Bresnan.
Ben Duckett also went cheaply to Bresnan but it was the intervention of Lyth that really unsettled the hosts. The gentle off-spinner had Libby caught at long-on and then dismissed Tom Mores and Clarke with successive deliveries.
Samit Patel and Fletcher also went to Lyth in the final over but Christian had hit David Willey for 6-4-6 to end the previous over to make the total competitive.
Notts needed to build early pressure, having posted a sub-par score and they grabbed two wickets from unlikely sources.
Patel threw down the stumps to run out Tom Kohler-Cadmore and then Jake Libby, bowling for the first time in T20 cricket, bowled Willey.
Lyth backed up his performance with the ball with a disciplined innings before slicing Gurney into the hands of Duckett at backward point.
The visitors needed 18 runs from the last two overs but Fletcher yorked both Jack Leaning and Bresnan.
Will Fraine hit Gurney for six at the start of the last over but the former England left-armer struck back, holding his nerve to pick up a wicket and three other dot balls in a dramatic climax.
Yorkshire coach Andrew Gale said: “I managed to catch a little bit of the Ashes earlier and what a knock from Ben Stokes at Headingley to get England over the line. The fantastic summer of cricket continues but here, it’s been very disappointing for Yorkshire.
“This is a game that we played some very good cricket in and probably should have got over the line but credit to Notts, they grind those sorts of results out on their own patch and we crumbled a bit under the pressure at the end.
“I think 85 per cent of the game we played some smart cricket. That sums up our one-day cricket, we can’t get over the line. We’ve tied three games and lost by a run in one of them and until we stand and take responsibility in key moments under pressure then we are where we are.”