Brathwaite picked up two wickets in two balls in the 91st over, claiming Durham’s second bonus point, with Clarke caught by Muchall in the slips on 49 and his replacement, Ambrose caught behind first ball.
He claimed his fourth wicket of the innings in the penultimate over of the day when Troughton was caught behind on 76.
At the close Warwickshire were 345-7, Best 0* and Woakes 16*.