Middlesex 423 (Robson 134, Holden 119*, Palladino 4-92) and 199 for 7 dec (Robson 73, Critchley 4-60) beat Derbyshire 295 (Critchley 105, Harris 4-83) and 210 (Murtagh 4-55, Bamber 3-35) by 117 runs
Tim Murtagh finished with 4 for 55 as Middlesex ran through the Derbyshire batting to secure a 117-run victory in their final home County Championship match of the season.
Murtagh - who passed 750 first-class career wickets in the process - finished the visitors off in the seventh over after tea, despite an unbeaten century from Derbyshire skipper Billy Godleman.
Although Godleman carried his bat for 105 from 147 balls at Lord's, it was not enough to deny his former county a victory that enabled them to leapfrog Derbyshire into fourth place in the Division Two table.
Middlesex declared on their overnight total of 199-7, setting the visitors a fourth-day target of 328, and they might easily have made deep inroads during the early overs.
Godleman played and missed, as well as surviving three appeals, but he gradually settled down and looked particularly strong on the off-side as he advanced towards his half-century.
It was Murtagh who made the breakthrough for Middlesex, tempting Luis Reece (12) into the hook shot and Ethan Bamber held a tricky catch at deep square leg.
The home side continued to take wickets at regular intervals, with James Harris trapping Wayne Madsen leg before and Martin Andersson finding the outside edge of Alex Hughes before lunch.
Although a brief downpour delayed the resumption, Murtagh struck again with his first ball of the afternoon, having Harvey Hosein caught behind as Derbyshire's scoring rate slowed dramatically.
At the other end, Bamber bowled a tight, consistent spell, and deservedly collected the wicket of first-innings centurion Matt Critchley, pinned in front of his stumps for eight as the visitors slid to 123 for 5.
Gary Wilson proved slightly harder to dislodge, sharing a sixth-wicket partnership of exactly 50 with Godleman before Harris sent his off stump flying with the next delivery.
With Derbyshire 189 for 6 at tea, every result remained possible heading into the final session - but Middlesex soon cemented their advantage by capturing the remaining four wickets inside half an hour.
Murtagh's first delivery of the session proved lethal once again, with Anuj Dal leg before for 14, and Bamber (3-35) then removed Hardus Viljoen and Tony Palladino in rapid succession.
Godleman did manage to complete the 12th century of his Derbyshire career in style, advancing down the wicket to drive Murtagh for a six over long-off.
But Derbyshire's cause was well and truly lost by then and Murtagh sealed the result by bowling last man Lockie Ferguson.