Warwickshire were six points better off than their opponents in the early Division One table after three matches, and they edged the morning as Yorkshire reached lunch at 97-4.
Having left Fin Bean out, Yorkshire used Dom Bess as a locum opener alongside Adam Lyth, who contributed 26.
Bess, for 16, was first to go when he got an inside-edge to a Bamber delivery which nipped back and was caught behind.
Smith took three morning catches, including James Wharton off Bamber at the second attempt. He fumbled the initial chance but held the rebound between his thighs.
When Root played at a back-of-a-length delivery from Barnard which he probably did not need to, edging low to second slip, Yorkshire were 32-3.
Lyth followed to Hannon-Dalby before Brook made an action-packed start to his innings. Although he drove nicely, he danced down the pitch twice looking to hit over the top and survived a huge caught behind appeal off Michael Booth.
Brook failed to add to his lunchtime 33 when miscuing an attempted uppercut off Bamber to Hamza Shaikh at third – to leave the score 97-5, three balls into the afternoon.
George Hill followed shortly afterwards to the same bowler before Bairstow and Jordan Thompson united to share a vital seventh-wicket 61, as Thompson supported his captain with 35.
There were signs of Bairstow – making his 100th Championship appearance – at his savage best. But there was finesse too. One straight drive off Barnard was as good as any shot all day.
However, Barnard removed both as Yorkshire fell to 185-9. Thompson was caught behind before Bairstow played on.
New Zealand bowler Ben Sears then clobbered a late 28 to sneak Yorkshire beyond 200 before edging Bamber into the slips.
