The Vikings never recovered from losing three wickets to the off-spin of skipper Wes Durston in the first five overs and, although Glenn Maxwell scored 45 from 29 balls and Jack Leaning 37 from 22, the visitors could only manage 146-9.
Hamish Rutherford smashed 40 from 24 balls in front of a sell-out Queen’s Park crowd of 4,500 and Wayne Madsen added 41 from 38 balls as the Falcons reached their target in the 19th over to end a run of seven consecutive home defeats against Yorkshire in T20 cricket.
The Vikings promoted Adil Rashid to open in place of Aaron Finch, who was ruled out with a foot injury, but he made only seven before he was stumped trying to hit Durston through the offside.
Durston struck again in the same over when Alex Lees was bowled and Yorkshire were in serious trouble when Andrew Gale had his leg stump knocked back aiming to lift Durston over mid-wicket.
Yorkshire’s first boundary did not come until Glenn Maxwell drove the last ball of the fifth over past mid-off and the batsmen struggled to get the ball away until Johnny Bairstow lifted Alex Hughes over long off for six.
Maxwell took two fours off fellow Australian Nathan Rimmington as the Vikings reached 60 for three at the halfway point and he drove Hughes over extra cover for six before Bairstow was caught sweeping Greg Cork for 22.
When Maxwell was bowled by Shiv Thakor, Yorkshire were 88 for five and in danger of falling well short of a competitive total and Tim Bresnan’s attempt to clear the ropes only ended in the hands of deep mid-wicket.
Leaning and Liam Plunkett plundered 17 off the 18th over from Cork, but three wickets fell in the final over leaving the Vikings with what looked a below-par total on a small ground.
Durston launched his team’s chase by lofting Maxwell’s second ball over mid-wicket for six and, although Matthew Fisher knocked out his leg stump in the second over, Hamish Rutherford drove Maxwell over the pavilion in the fifth over.
Chesney Hughes was lbw sweeping at Maxwell but the over cost 16, including five wides, and Rutherford took four fours from Josh Shaw’s first over as the Falcons accelerated towards their target.
The New Zealander drove a return catch back to Liam Plunkett and, although Thakor was run out, the Falcons appeared to be cruising until Madsen was caught behind and Billy Godleman was needlessly run out in the 17th over.
But Alex Hughes eased the pressure by pulling Plunkett for six and Derbyshire recorded only their second T20 win in 10 games at Queen’s Park with seven balls to spare.
Yorkshire’s director of cricket Martyn Moxon said: “I felt we had a chance if we bowled and fielded well but we didn’t bowl well enough as a group - there were too many easy ‘four’ balls and it was a pretty disappointing performance all round.
“The bottom line is we are not playing well enough in this form of the game.”
“That gives us a lot of confidence, to beat a strong Yorkshire side,” Durston said. “I don’t think I could have gone through another meeting where we were talking about how we should have won.
“We know we’ve got the players to do it - it’s about having the belief and although I got the man of the match, that was for the team.”