Bresnan removed Warwickshire captain Varun Chopra, who was drawn forward by a fine delivery that he edged to wicketkeeper Andrew Hodd.
But the pace bowler missed a chance to get his name on the scorecard for a second time when he put down William Porterfield at third slip off Matthew Fisher.
It was a regulation chance to Bresnan’s right and Porterfield had 19 at the time with the total on 34-1 in the 17th over.
Porterfield (35) and Ian Westwood (54) fought back well after the early loss of Chopra, lifting their side to 91-1 at lunch.
James Middlebrook, the 37-year-old off-spinner drafted in as cover for England’s Adil Rashid, has so far bowled five overs from the Rugby Stand end, which have yielded 17 runs - including a straight six by Porterfield. Middlebrook - who last played for the club in 2001 - went straight into the side after being drafted in as a short-term replacement for England’s Adil Rashid.
The 37-year-old off-spinner is the only change to the Yorkshire team that drew with Nottinghamshire at Trent Bridge, with Rich Pyrah dropping to 12th man.
Warwickshire won the toss and opted to bat in sunny conditions.
Yorkshire: Lees, Rhodes, Pujara, Gale (capt), Leaning, Hodd, Middlebrook, Bresnan, Patterson, Brooks, Fisher.
Warwickshire: Chopra (capt), Westwood, Porterfield, Evans, Hain, McKay, Clarke, Barker, Patel, Wright, Rankin.