Having declared on 505 for nine on day two, the White Rose claimed four wickets for 98 runs to leave the visitors 190 for five at lunch.
Opener Nick Compton (33) was first out to fellow England player Tim Bresnan, who struck with the second ball of the morning and also added the wicket of Jack Leach (eight). All-rounder and first-innings centurion Adil Rashid then added the wickets of Alviro Petersen, who made 54, and Arul Suppiah (nought).
On day two at Edgbaston, Middlesex opener Sam Robson reached the interval on 185 not out against Warwickshire.
Robson began on 136 and added 49 runs against a Bears attack hit by injury and England Lions call-ups.
Boyd Rankin and Jeetan Patel both managed a wicket apiece, though, as Middlesex moved to 373 for five.
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- Nick Compton