Yorkshire were denied the chance to open up a 16-point lead at the top of the LV= County Championship table when Durham showed gritty determination in batting out the final day at Headingley.
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The main consolation for Yorkshire was that the 13 points they gained from the draw placed them five points ahead of second-placed Nottinghamshire.
Although Yorkshire never gave up, Mark Stoneman (86), Michael Richardson (95) and Phil Mustard (57 not out) all made major contributions as Durham reached 323 for eight to lead by 128 with only 11 overs remaining.
Durham, 59 for one overnight, began the final day still trailing by 136 runs and Yorkshire's hopes rose as the first ball of the second over from Jack Brooks was allowed to thump into his pads by Scott Borthwick, who offered no stroke to a straight delivery.
Although qualms had already been expressed by Durham skipper Paul Collingwood over the unpredictable state of the pitch, Stoneman and Richardson coped more than adequately against both pace and spin.
Boundaries on either side of the wicket for Stoneman off consecutive balls from Tim Bresnan boosted the score but there was a fortunate moment for Richardson when he drove Steven Patterson into the covers and Bresnan flung himself at the ball but could not hold on.
With skipper Andrew Gale regularly ringing the changes, Adam Lyth came on for another short spell of off-spin and his fourth ball trapped Stoneman lbw for a solidly fluent 86 which contained 10 boundaries and came off 165 deliveries.
The opener's departure ended a tenacious stand of 86 in 25 overs with Richardson, who survived another very sharp chance as his thick edge off Patterson ricocheted off Jonny Bairstow's gloves as the wicketkeeper dived far to his left.
Richardson and Gordon Muchall took Durham to lunch on a comfortable 163 for three, only for Yorkshire's hopes to rise again in the first over upon the resumption, Adil Rashid's well pitched up googly to Muchall gaining an lbw decision.
Durham were 166 for four and still not quite out of the woods but now Collingwood, unbeaten on 64 first time around, joined Richardson in another determined stand during which Richardson moved to his 50 off 99 balls with five fours.
They slowly wiped off the deficit and Richardson took the visitors into the black by stroking Rashid to the extra cover boundary - but with Durham on 210 the leg-spinner got sufficient turn and bounce for Collingwood to edge to Bairstow.
The new ball was taken at 228 for five in 81 overs and it brought about Richardson's downfall just five runs short of a deserving century.
Brooks breached his defences to hit middle and leg after the batsman had received 165 deliveries and struck 11 fours. His 95 followed his 148 against Yorkshire at Chester-le-Street in early May.
Soon after tea, at 261 for six, John Hastings survived a fierce return catch to Rashid but failed to make the most of it because he flicked a delivery off his glove from Brooks and was caught behind.
Brooks further revived Yorkshire's situation by having Phil Coughlin lbw with a yorker - 95 ahead with 24 overs remaining - but Mustard continued to hold things together until all realistic chances had evaporated for Yorkshire.
Mustard's half-century came off 73 balls - and he was still there with 57 when Yorkshire finally threw in the towel.
Gale said: "It feels almost like a loss after dominating the game for large periods and then not getting over the line but there were a lot of positives - like going top of the table with five games remaining.
"I thought we put the ball in good areas consistently but some half-chances went down and we were sloppy in the field in the afternoon.
"Fair play to Durham because they battled hard - but they were never going to lie down and die. They battled really hard on a tough pitch.
Richardson said: "Sometimes I haven't done well coming in on the back of big partnerships. I prefer coming in under pressure because it narrows the mind.
"We were staring down the barrel and knew we had to bat all day."