Craig White's unbeaten 135 was the difference between the sides on a run-feast of a day at Chester-le-Street, in which 437 were scored.
Shoaib Akhtar had threatened to tear through Yorkshire's tail when he dismissed Andy Gray for his overnight 60, and Darren Gough and Ryan Sidebottom didn't last too long either. But Steve Kirby hung around long enough for White to play a few shots, and Yorkshire's total of 448 was more than satisfactory.
Durham in reply managed a healthy 327, but a first-innings deficit of 121 may come back to haunt them. Three Durham batsmen made half-centuries, but none exceeded Gary Pratt's 54, as Kirby followed his good work with the bat with 4 for 93. Gough, with a Test recall up for grabs, was lively in his 18 overs, but managed just the one wicket, that of his namesake, Michael.