At tea on day three, Warwickshire are 95-3 in their second innings, with Jonathan Trott unbeaten on 53 and Tim Ambrose undefeated on 32.
The pair have added 81 for the fourth-wicket in a fighting stand.
After the visitors resumed on 0-1 after lunch, with Ryan Sidebottom having trapped Andy Umeed lbw with the fourth ball of the innings, Warwickshire lost two wickets with the total on 14.
Jack Brooks had Varun Chopra lbw for four with the first delivery of the 10th over, and the pace bowler struck again three balls later to pin Ian Bell in front for a duck.
At that stage, Yorkshire were well on top, and it might have been 30-4 but wicketkeeper Andy Hodd could only get fingertips to a difficult, high chance when Ambrose, on nine, edged Tim Bresnan.
Ambrose was batting ahead of Sam Hain, who had earlier damaged his shoulder while fielding on the boundary.
Trott has glued the Warwickshire innings together and played a number of handsome shots, including a cover-driven four off Steve Patterson.
Yorkshire introduced Travis Head into the attack shortly before tea, the Australian batsman turning his off-breaks prodigiously, with leg-spinner Adil Rashid operating from the opposite Rugby Stand end.
The pitch remains challenging to bat on, with all results possible.