Alex Hales and Samit Patel struck 54 and 52 respectively as Notts won the toss and posted a handy total of 172 for six despite their innings never truly catching fire.
Derbyshire seamer Shiv Thakor counted Patel among his scalps in an impressive return of 3-25, while Hamish Rutherford became the game’s third half centurion at the top of the visitors’ response.
Jake Ball came in for early punishment but the ragey Notts right-armer pulled his figures back to a man-of-the mach haul of 3-36, including the vital wicket of Rutherford for 62, and Trent Bridge’s record domestic T20 attendance of 13,582 were treated to a final-over shootout.
With five needed from the last delivery, Wayne Madsen could only managed two from a well-directed Harry Gurney yorker - drawing scant consolation a fine 51 not out as his side reached 170 for four.
Notts move onto 10 points, with trips to Lancashire, Durham and Leicestershire to conclude their North Group campaign, while Derbyshire remain bottom of the standings.
Hales began with a brace of fours off Wes Durston but opening partner Michael Lumb did not start in such fluent fashion, chipping Thakor to deep midwicket.
The next catch came in the crowd as Hales dispatched Thakor over his favoured square-leg region, while new man Riki Wessels dished out similar treatment to Nathan Remmington before Greg Cork dismissed him for a breezy 22..
Hales greeted Chesney Hughes’ left-arm spin at the halfway mark by shovelling four - Notts’ first boundary since the fifth over, which was followed by Patel handsomely planting Alex Hughes beyond long-on in consecutive overs.
A cut behind square from Hales brought up the fifty partnership in between those blows and back-to-back fours saw the opener raise his own half-century from 33 deliveries. He could not kick on, holing out to Alex Hughes off namesake Chesney.
Patel carved a four over extra cover to move towards a 35-ball fifty, although Thakor removed him at the start of the 18th when Tom Knight held a steepler.
James Taylor become Thakor’s third victim for 12 when an attempted ramp shot spooned up to wicketkeeper Tom Poynton and Rimmington yorked Steven Mullaney at the start of a superb closing over that cost six.
Durston got Derbyshire off to a flyer but, having thrashed four fours off Ball he hit the same bowler to Gurney at third man to fall for 22.
Rutherford hoisted Gurney over wide long-on and crunched the next delivery through the covers as the Falcons soared past 50 after five.
Mullaney (1-23) snaffled Chesney Hughes caught and bowled to end a 43-run stand at the end of the eighth and Derbyshire had slowed to 83 for two midway through the chase.
Rutherford reached a 40-ball fifty and added 57 with Madsen before Ball pivotally uprooted the New Zealander’s middle stump halfway through the 16th over.
Alex Hughes lost his leg stump to Ball and Derbyshire needed 11 from the final over - a task that proved just too steep for the unfortunate Madsen.