Ashwell Prince got the Lancs innings back on course after a quick stumble
Lancashire made it five wins from five at Old Trafford to maintain their 100% Twenty20 Cup record as Derbyshire suffered a third straight defeat.
Openers Paul Horton (41) and Tom Smith (32) gave the home side a great start before Ashwell Prince (38no) got things back on course after a fall of wickets.
But Derbyshire did not even threaten the North Division leaders' 165-7.
England paceman Sajid Mahmood took four wickets as the visitors, showing little urgency, limped to a halt on 127-9.
It was the rapid opening partnership of 75 from 40 balls between Horton and Smith, both of whom hit Twenty20 career-bests, that set Lancashire on their way.
Horton hit 41 from 20 balls, including seven fours and a six, while Smith cracked three fours and a maximum in his 21-ball 32.
It was only the introduction of medium-pacer Garry Park and leg-spinner Mark Lawson, who removed both Horton and Smith in consecutive overs, that slowed the Lancashire onslaught.
Derbyshire's comeback then gathered further pace when in-form Francois du Plessis was stumped off the bowling of off-spinner Greg Smith for five, three balls into the 11th.
But Steven Croft helped Prince get things back on course with a fourth-wicket partnership of 51.
Derbyshire were then undone in the first three overs of their pursuit of 166.
Tom Smith removed Greg Smith in the second and Glen Chapple (2-11 off three) got Jamie Pipe in the next to leave the Phantoms in the mire at 16-2. And Mahmood ripped out Australian Chris Rogers' off and middle stumps to leave them 36-3.
Lancashire's continued plan of switching their bowlers regularly gave the Derbyshire batsmen little chance to settle.
And, although Wavell Hinds (32 off 31 balls) and John Sadler (23) both stayed there, Mahmood further put the brakes on with three late wickets.
Having maintained their four-point lead at halfway in the group, Lancashire's next test is at home to Durham at Old Trafford on Thursday (1730 BST).
Lancashire coach Peter Moores told BBC Radio Lancashire:
"We're playing really good cricket, both with bat and ball.
"We got a good start through Tom Smith and Paul Horton and then Ashwell Prince took us to a score that I thought was above par.
"The players have begun to understand the roles we want them to play. Glen Chapple's decision making has been very good and these things have blended to result in the good start we've had."
Derbyshire all-rounder Garry Park told BBC Radio Derby:
"They came out hitting hard and it came off. They had 60 up in no time at all.
"Once we started clawing it back it changed the game a little.
"But that first five or six overs killed us off. If you took that away it could have been a different game."
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