Andrew Gale's decision to bowl first paid handsome dividends as the home team stuttered to 90-5 at lunch.
Ajmal Shahzad was Yorkshire's most successful bowler, taking 3-30.
He was well supported by Tim Bresnan, who was unlucky to take only one wicket, and Steve Patterson, who bowled a miserly opening spell of 7-3-15-1.
Beneath overcast skies, Durham lost their first wicket in the fourth over when Patterson had Mark Stoneman caught behind for one.
Durham fell to 32-3 when Shahzad struck twice in the last three balls of his opening over, having Gordon Muchall lbw for 12 and uprooting Dale Benkenstein's off-stump with a beauty that left him.
Bresnan got in on the act when he had Ian Blackwell smartly caught by Jonathan Bairstow at third slip for six, the bataman aiming an airy drive.
And Durham plunged to 54-5 when Shahzad won an lbw verdict against Ben Stokes, who fell for a sixth-ball duck.
Opener Michael Di Venuto batted through the session to score 43, while Phil Mustard - after surviving several close lbw calls against Bresnan - is undefeated on 21