Current County Championship leaders Middlesex also won, however, to leave it increasingly likely that the title will be decided when the two teams meet at Lord’s on September 20.
Chris Rushworth was last man out for the visitors, bowled by Jack Brooks for six as Durham were dismissed for 192.
Middlesex increased the relegation pressure on hosts Nottinghamshire at Trent Bridge, when they chased down their target of 235 to win by five wickets.
Earlier on day four it was veteran Ryan Sidebottom who did tha damage, taking three wickets in 18 balls in the morning session.
After Durham resumed on 39-3, chasing 421 to win, Sidebottom reduced them to 63-6.
First, he had nightwatchman Graham Onions caught for six by Gary Ballance in the covers and then he trapped Scott Borthwick and Paul Collingwood for nine apiece.
After Sidebottom’s triple salvo, Yorkshire were held up by the seventh-wicket pair of Graham Clark and Michael Richardson, who battled hard in cloudy conditions.
Richardson defended solidly and attacked selectively, driving Jack Brooks to the cover boundary, and Clark also played some nice strokes, including a pull to the boundary off Brooks.
But with the stand worth 49 in 19 overs, Tim Bresnan made the all-important breakthrough when he had Clark caught behind for 25.
Richardson was next to go, caught by Bresnan to give Sidebottom his fourth victim for a stubborn 33, before Barry McCarthy and Rushworth both followed cheaply.