A half century from skipper Andrew Gale and an unbeaten 48 from former Derbyshire batsman Gary Ballance took the visitors to their target of 138 with four balls remaining.
Clint McKay wrapped up victory in style with a six - only the second of the match - off Tim Groenewald but the Falcons' hopes of making the last eight had already been ended by Northamptonshire's win against Durham.
Derbyshire's batsmen struggled on a slow pitch with Wes Durston's 39 from 35 balls the top score in a below-par total of 137 for seven.
The Falcons went into their final North Group game without big hitting South African batsman Loots Bosman who was out with an injured knee and his replacement, Chesney Hughes, shared an opening stand of 41 with Durston.
Hughes struggled to get the ball away and made 14 in seven overs before he was bowled swinging at Richard Pyrah and Greg Smith went in the next over when he came down the pitch to Adil Rashid and was bowled.
The Falcons hit only four boundaries in the first 10 overs and their hopes of raising the tempo in the second half of the innings suffered a blow when Durston slapped a wide full toss from Lee Hodgson to short cover.
Derbyshire were in danger of falling short of a competitive total when Jon Clare was bowled by Hodgson for 10 and Wayne Madsen was lured down the pitch by David Wainwright and stumped by yards.
The first six of the innings came in the 18th over when Garry Park latched on to a long hop from Wainwright and some clever improvisation from Robin Peterson, whose unbeaten 32 from 24 balls included three fours, at least gave the Falcons a decent score to defend.
The Falcons' hopes soared briefly when Adam Lyth pulled a low full toss from Smith to deep midwicket in the second over and there was more encouragement for the home supporters three overs later.
Herschelle Gibbs played one crunching straight drive for four off Groenewald but he went for another big shot off the next ball and skied a catch to extra cover.
At 30 for two, the game was wide open but Gale and Ballance tilted it towards Yorkshire with a stand of 85 in 13 overs although Derbyshire had a strong run-out appeal rejected in the 14th over when Gale was on 41.
By the time Gale departed for 55 from 56 balls, bowled moving across his stumps trying to work Charl Langeveldt through midwicket, the game was slipping away from the home side although Yorkshire wobbled briefly before crossing the line.
Jonathan Bairstow was needlessly run out going for a second in the penultimate over but McKay settled any nerves by lifting Groenewald over deep square leg to win what had been a strangely flat game in front of a disappointingly low crowd.