First-innings centurion Gary Ballance, Adam Lyth and Tim Bresnan all fell for single figures as the County Champions slipped to 147 for six in their second innings, a precarious lead of 123.
Lyth and Bresnan’s England days seem to be over, but Ballance is pressing for a recall after being a non-playing member of the Test squad that toured South Africa this winter.
Will Rhodes, who narrowly missed out on a first-innings ton, and Andy Hood came to the rescue with a seventh-wicket stand of 80 that was broken shortly before stumps on day three.
Yorkshire closed on 239 for seven, 215 ahead, with Rhodes unbeaten on 41, shortly after Hood went lbw to Jake Ball for 44.
Earlier Andrew Gale’s side quickly wrapped up the MCC first innings, conceding a deficit of just 24.