Adil Rashid struck three times in the afternoon as Yorkshire kept the pressure on Durham during day three at Headingley.
Durham, beginning after lunch on 119-5 in reply to 426, have reached tea at 225-8 from 85 overs, with captain Paul Collingwood still unbeaten on 61. Durham, 201 behind, need 52 to avoid the follow-on.
Rashid had Phil Mustard caught at short-leg by Jack Leaning for 17, thus ending a sixth-wicket stand of 51 between him and his skipper and leaving the visitors at 170-6 in the 71st over.
The leg-spinner then had John Hastings caught at slip by Adam Lyth with a ball that popped from a good length as Durham fell to 174-7, and they were soon 194-8 when Paul Coughlin lofted the same man to Jack Brooks at long-on in the 79th over.