Yorkshire 171 for 4 (Root 60*, Brook 50*) beat Derbyshire 167 for 6 (Wood 67, Godleman 49, Coad 3-40) by six wickets
Root scored an unbeaten 60 from 50 balls while Brook smashed 50 off 29 to take the Vikings to their target of 168 and end a run of four straight T20 defeats.
They looked to be heading for another disappointment when Sam Conners removed Adam Lyth and Dawid Malan in the space of three balls and were well off the pace at 80 for 4.
But Root and Brook shared an unbroken stand of 91 to overhaul the Falcons 167 for 6 which was built around a T20 best of 67 from 48 balls by Tom Woodwith Ben Coad taking 3 for 40.
The Falcons, who finish bottom of the North Group, looked on course for a bigger total after Wood and skipper Billy Godleman plundered 80 from the first 10 overs.
Wood ramped Coad for six and cut the seamer for four as 20 came from the third over and he reached his first T20 50 off 31 balls by pulling Root onto the Western Terrace for another maximum.
Godleman swept Root to backward square in the 14th over and although Wayne Madsen marked his 500th innings for Derbyshire by launching Jordan Thompson over long on for six, the Falcons lost momentum in the closing overs.
Coad completed an excellent comeback by having Wood caught at deep wicket and Leus du Plooy edged behind swinging at Thompson to give wicketkeeper Ben Birkhead his first Blast victim on debut.
Madsen was well caught by Lyth at extra cover and Matt Critchley could only sky his first ball to mid-off.
After Alex Hughes pulled Duanne Olivier to deep square, Luis Reece took consecutive fours off the South African but it had been a good recovery by the Vikings bowlers who kept their discipline to restrict the Falcons to 32 from the last four overs.
Lyth started the chase with two boundaries from Madsen's opening over but Conners struck two huge blows in the third.
The Vikings skipper top edged a pull and was caught behind and Malan went two balls later when he got an inside edge driving at Conners.
Will Fraine responded by pulling Madsen for six and Root pulled and clipped Conners for successive fours but the Vikings suffered another blow in the 6th over; Fraine chipped Dustin Melton to midwicket and at the halfway point, the Vikings were well off the pace, needing another 103 runs.
Thompson opened the throttle by pulling Critchley for six as 13 came from the 11th over but he holed out to long-off in the next.
Root launched Reece over the long-on boundary as 20 came from the 15th and Brook twice dispatched Conners for two fours to reduce the target to 33 from three.
Brook drilled Melton for six over long-off and when it came down to nine off the last, Brook lofted the final ball for four to end a disappointing Blast campaign on a positive note.