Middlesex 423 (Robson 134, Holden 119*, Palladino 4-92) and 199 for 7 (Robson 73, Critchley 4-60) lead Derbyshire 295 (Critchley 105, Harris 4-83) by 327 runs
Matt Critchley became Derbyshire's youngest ever centurion at Lord's - but his side will face an arduous challenge to overcome Middlesex on the final day of their County Championship clash.
The 22-year-old all-rounder top-scored for the visitors with 105 before picking up four wickets as Middlesex ended day three with a healthy advantage of 327 runs.
Critchley's ton made him the youngest Derbyshire player to achieve three figures at Lord's - Stan Worthington was eight months his senior when he scored 101 on the ground 90 years earlier.
Despite Critchley's efforts with both bat and ball, Middlesex hold the upper hand after Sam Robson's knock of 73 enabled them to reach 199 for 7 in their second innings.
After a morning downpour had delayed the start by an hour and a half, Critchley immediately set about knocking off the 52 runs still required for Derbyshire to avoid the follow-on.
Resuming on 87, he drove James Fuller for successive leg-side boundaries and then cut another four past gully to bring up his century. But James Harris (4 for 83) regained the initiative for Middlesex, persuading Critchley to attempt a hook shot that somehow sailed into the hands of second slip, and then removing Anuj Dal and Tony Palladino in quick succession.
However, Hardus Viljoen, with an unbeaten 31 from 25 deliveries, and Lockie Ferguson threw the bat as they put together a crucial last-wicket partnership of 43.
Ferguson smote Tim Murtagh back over his head for six to save the follow-on before the Middlesex bowler took revenge, uprooting his off stump as Derbyshire were dismissed for 295.
Boosted by his first innings century, Robson looked in good nick again as Middlesex began the task of extending their lead of 128 as swiftly as possible.
Robson went for his shots on both sides of the wicket, displaying sound timing and dominating an opening stand of 58 with Nick Gubbins, ended in bizarre fashion when the left-hander dislodged his bails while attempting to leg-glance Ferguson.
Critchley then regained centre stage with his leg-spin, bamboozling Stevie Eskinazi for a leg-side stumping and having Dawid Malan caught after his sweep struck close-range fielder Gary Wilson and ballooned up to backward square.
And Critchley also accounted for Robson on the stroke of the tea interval, running the opener out from mid-off after he had been sent back by Max Holden to end his hopes of completing a second ton in the match.
Holden was one of two further victims to fall to the leg-spinner in a truncated final session, but Martin Andersson accumulated an undefeated 23 from as many balls, increasing Middlesex's lead beyond 300 before bad light brought play to a premature close.