Resisted in their attempt to force a victory at the Rose Bowl in the first round of matches, Durham pressed home their advantage successfully here, although only after Yorkshire had mounted a belated show of resistance.
Having lost two wickets on Saturday evening after being set a theoretical 490 to win, Yorkshire had slipped to 176-6 at lunch yesterday and there was little expectation that Durham would be detained much longer.
But that assessment was based on another below-par performance from the senior members of Yorkshire's top order and did not take into account the capacity of Rich Pyrah and Ryan Sidebottom to show a little mettle.
In the end, largely due to the former's best score in Championship cricket, it was 16 minutes into the final hour before Scott Borthwick, the young Durham leg-spinner, obtained the lbw verdict against Pyrah that ended the game.
Earlier, Jonathan Bairstow (pictured), who combines his late father's combative nature with the elegance and timing of a high quality stroke-player, had made a 118-ball 81 of style and character, but it seemed unlikely to be an innings of any significance in terms of the outcome.
He and Pyrah shared a partnership of 67 before Borthwick, finding turn and bounce from a pitch that had held together well, nicked the edge of Bairstow's bat with a ball that spun away from the right-hander, Michael di Venuto taking the catch at slip.
But, at 225-7, rather than hasten Yorkshire's demise, Bairstow's exit prompted Pyrah, a number eight with two first-class hundreds to his name, to show that he too could be stubborn if circumstances demanded it. Joined by Ryan Sidebottom, whose 61 at Worcester last week revealed a part of his game not often seen, the 28-year-old seam bowler proved so resistant to Durham's various efforts to prise him out that a draw for Yorkshire began to look at least a possibility, even if a remote one.
Durham's bowlers seemed to be running out of steam, with Graham Onions, buoyed by his five-wicket comeback on Friday, bowling well but unable to add to the early dismissal of Joe Root, the young opener whose form was the bright spot for Yorkshire.
When Liam Plunkett, from his usual mixed bag, produced one of his better balls to force Sidebottom to edge a fifth catch of the innings to stand-in wicketkeeper Michael Richardson, the pair had batted for 33 overs and put on 98.
Steve Patterson went next ball, more or less sealing Durham's win with 21 overs still to play, but Pyrah kept going for another 11 overs before a Borthwick googly was adjudged to have trapped him leg before, 13 away from what would have been a deserved hundred.
Borthwick, 20, finished with 3 for 49, his wickets – Andrew Gale, Bairstow and Pyrah – arguably the key ones from what Durham coach Geoff Cook described as "an outstanding spell of leg-spin bowling". Durham will assess how much the match has taken out of Onions before deciding if he can play against Sussex on Wednesday.