Play started at Headingley with Yorkshire advancing their first innings from 465-9 to 475 all out.
Jordan Thompson moved from 44 to 50 and was last man out to Ben Raine, drilling a catch to long-off to give the Durham seamer excellent figures of 5-76.
When Thompson reached his fifty off 112 balls, he tapped the white rose on his chest with his bat in an obvious acknowledgement of his love for his home county ahead of a winter move to Warwickshire.
Having scored a first-innings 101, Raine became the fifth man in Durham’s first-class history to hit a century and return a five-wicket haul in the same match.
And with their task clear, there was absolutely no need for adventure with the bat in their second innings.
They reached lunch at 27-1 in 23 overs, losing Emilio Gay caught behind off the inside-edge pushing forwards at Hill.
But then came the drama as Durham lost their last nine wickets for 56.
Bess had Alex Lees caught behind for 18, pushing forwards just after lunch, a beauty of a delivery to the left-hander.
And when Thompson’s seam accounted for Ben McKinney and David Bedingham, lbw and caught behind in successive overs, Durham were 62-4 in the 35th.
Hill trapped Ollie Robinson lbw with one that kept low shortly afterwards and struck again in his next over to have Graham Clark caught at backward point for his 50th Championship wicket of the season.
Durham were 76-6 and it took less than four more overs for the game to finish in deteriorating light.
Raine miscued to mid-off as he tried to hit Bess over the top before Matthew Potts was caught at short-leg and Daniel Hogg edged behind – all three wickets falling in the 44th over.
Will Rhodes was then trapped lbw by Hill to finish the game, the last four wickets falling for two runs in only 10 balls.
Yorkshire were jubilant, especially Hill with 4-14 and Bess 4-22, while Durham were disconsolate, and it will take some time to work out how they let this one get away.
Match report supplied by ECB Reporters’ Network, supported by Rothesay
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