Derbyshire collapsed to 60 all out, including a hat-trick for Toby Roland-Jones, as Middlesex claimed their second straight victory to start the County Championship season.
The visitors actually made a good start to day three at Lord's, Jonathan Clare (4-40) taking two of the four wickets needed to polish off Middlesex's first innings for 215 and claim a lead of 16.
But Middlesex's seam attack proved altogether too much second time around; Shivnarine Chanderpaul was left stranded on 18 in a Derbyshire innings lasting 35 overs.
Tim Murtagh claimed 5-12 in 12 overs and was well supported by new-ball partner Steven Finn (2-34) before Roland-Jones (3-4) took centre stage, removing the last three - Tony Palladino, Tim Groenewald and Mark Turner - with successive deliveries.
West Indies left-hander Chanderpaul, batting at number four, resisted for 78 balls but received little support with opener Wayne Madsen (15) and wicketkeeper Tom Poynton (10) the only others to reach double figures.
Middlesex overcame the early loss of Sam Robson to power to a target of 77 and seal a nine-wicket victory thanks to Chris Rogers (28no) and Joe Denly (44no).
After beating Nottinghamshire at Trent Bridge in their season opener last week, Middlesex are now the early Division One pacesetters with 43 points.