Warwickshire had the better of the second afternoon session at Headingley but Oliver Hannon-Dalby and Adil Rashid both struck before tea.
Yorkshire lost Tino Best and Hannon-Dalby soon after lunch to wrap up their first innings for 425.
They had started the day at 325-4, losing their last six wickets for 100 runs. The Bears then advanced their reply to 111-2 after 33 overs at tea.
Captain Ian Westwood and fellow opener Darren Maddy shared a stand of 102 inside 28 overs. Westwood recorded 66 off 95 balls, while Maddy reached 35 off 77.
But both batsmen were then trapped lbw in successive overs to leave the score 104-2 in the 29th.
Jim Troughton and Ant Botha were at the crease at the start of the evening session.
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