They were without six bowlers to a combination of injuries and international call-ups and were left to score 357 on the final day, which would have been the fourth-highest successful chase in their history.
With so many absences, Yorkshire would probably have settled for parity before the start of the game, the ultimate outcome after four days of stalemate.
But, depleted or otherwise, the champions played well enough to get themselves into a winning position and then not quite well enough to grasp the opportunity.
After a career-best 6-56 from Steve Patterson dismissed Durham for 172 on the first day, Yorkshire scored 323 in reply, thereby gaining a first innings lead of 151.
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They then reduced Durham to 105-4 in their second innings.
But a combination of resilient batting, an increasingly flat pitch, and some indifferent bowling from a scratch visiting attack saw the hosts reach 507-8 before they declared one hour into yesterday’s final day, leaving Yorkshire with a stiffer target than might have been the case.
Even so, it felt like Yorkshire were on top once more at 112-0 needing a further 245 from 48 overs, but the loss of two wickets in two balls on that score led to their challenge ultimately petering out, the total standing at 238-5 when the sides shook hands.
All results had been possible at the start of the day when Durham resumed on 452-8, a lead of 301.
Keaton Jennings, the tall South African-born opener, was 15 short of a maiden double hundred, which he duly brought up from 397 balls with 20 fours.
In hot sunshine, Durham eased past their previous best score against Yorkshire at this ground: 481 in 2007.
They could probably have gone on for much longer had Paul Collingwood not pulled the plug, Jennings finishing on 221 from 416 balls with 23 fours and Chris Rushworth on 31, the pair’s unbroken ninth-wicket stand worth 82 in 22 overs.
Collingwood was unable to direct events on the field after confirmation of a broken thumb sustained while fielding on day two.
Ben Stokes, stepping up his comeback from a knee injury, spent much of the match batting in the nets, where his presence regularly drew an excited horde of spectators.
The Chester-le-Street public seemed less excited to see Ryan Sidebottom and Jack Brooks in those nets yesterday, but visiting spectators were certainly cheered by the sight of two of Yorkshire’s injured clearly well on the road to recovery.
Left with 50 minutes’ batting before lunch, Yorkshire negotiated them without alarm to reach 38-0.
Eight balls into the afternoon session, Adam Lyth danced down the track and launched the leg-spin of Scott Borthwick for a straight six into the Lumley End.
It was a stroke that signalled Yorkshire’s intent, and Borthwick was made to look powder-puff by the opening pair.
Alex Lees won the race to fifty – his second of the match – from 76 balls with six fours, Lyth following suit from 100 deliveries with three fours to go with his six off Borthwick.
The dynamic of the day changed, however, when Yorkshire lost their first two wickets on 112 in the 33rd over.
Lyth, moments after reaching his half-century, was smartly taken above his head at first slip by Stokes off Barry McCarthy, who then trapped Kane Williamson lbw with one that nipped back. When Yorkshire lost Gary Ballance moments before tea and Andrew Gale shortly after it, survival became the order of the day.
There were still 23.4 overs left when Lees chopped on to Ryan Pringle to leave Yorkshire 179-5 after a fine innings of 74, made from 145 balls with seven fours.
But Jack Leaning and Tim Bresnan battened down the hatches in a stand of 59 in 26 overs.
The draw kept Yorkshire level on points with Lancashire at the top of Division One, with the Red Rose in first position by virtue of having won one more match.
Yorkshire and Durham lock horns again at Chester-le-Street tonight in the NatWest T20 Blast (6.30pm start). It is a meeting of the North Group’s bottom two clubs, and Yorkshire have named a 14-man squad as they seek to pull away from last place.
Yorkshire (from): Ballance, Bresnan, Carver, Coad, Gibson, Hodd, Leaning, Lees (captain), Lyth, Patterson, Rafiq, Rhodes, Shaw, Williamson.