They bowled the visitors all out for 375 with Nic Pothas taking his score to 118 not out.
In reply, Warwicks lost Darren Maddy for eight and then had Tony Frost run out for four with the score on 12-2.
John Trott made 22 and Ian Bell 29 before Jim Troughton and Tim Ambrose steadied the ship.
Stratford's Jim Troughton had reached his unbeaten century by the close, hitting 12 fours from 172 whilst Ambrose was not with 47 and Warwicks 224-4 after sixty overs.