Wayne Madsen added 36, before a 24-run ninth-wicket stand between Tim Groenewald (14) and David Wainwright (15*) helped Derbyshire post 115 from their allotted overs.
Wainwright (3-21) picked up two wickets in as many balls to give the hosts hope, but a composed innings from Michael Lumb (49 from 40 balls) and 34 from James Taylor moved the Outlaws to their 116 target with just 15 balls to spare.
After losing the toss, Derbyshire struggled with the bat, losing regular wickets, as Nottinghamshire took the early advantage after removing both openers inside three overs.
Shivnarine Chanderpaul and Madsen began the Falcons’ recovery, adding 36 runs together in six over, but the West Indies international was the third man out for 13 to leave the hosts 45-3 after eight overs.
Madsen continued his timely innings, running well between the wickets to add 36 from just 28 balls, before he was superbly ran out by Chris Read with a direct hit at the non-strikers end.
A flurry of wickets fell shortly after as the hosts slumped from 64-4 to 79-6 in the 15th over. The tail, however, once again added some valuable runs in the final overs to help Derbyshire post a slightly below-par total from their 20 overs.
A brisk unbeaten 15 from Wainwright and 11 from Tim Groenewald ran well between the wickets, while finding the boundary to push the Falcons onto 115-9 from their allotted overs.
Nottinghamshire made a blistering start courtesy of England opener Michael Lumb. The opener hit six fours inside the opening four overs to move the visitors onto 31-0.
But an exceptional over from David Wainwright gave the hosts renewed hope, as the spinner claimed two wickets in two balls to remove both Alex Hales (10) and Rikki Wessels (0) to leave the Outlaws 42-2 after six overs.
Michael Lumb, however, continued his excellent innings, ably assisted by James Taylor, as together they rotated the strike and ran well between the wickets to steadily move Nottinghamshire towards the victory target.
Together they added 50 runs to move the Outlaws onto 92 in the 15th over, before Lumb was ran out to top score with 49 from 40 balls.
The hosts claimed a fourth wicket soon after, as Wainwright – the pick of the Derbyshire bowlers – trapped Taylor lbw for 34. But it was ultimately in vain as David Hussey (11*) and Samit Patel (8*) guided the visitors to a six-wicket win with 15 balls overs to spare.
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