The hosts added 55 to declare on 507-8, as Keaton Jennings ended 221 not out.
It set Yorkshire 357 to win in 81 overs and Alex Lees and (74) Adam Lyth (50) put on 112 to raise hopes of a win.
But Lyth and Kane Williamson fell in successive balls to Barry McCarthy (2-27), while two wickets for Ryan Pringle (2-35) saw Yorkshire bat out a draw.
Second-placed Yorkshire are now level on 99 points with leaders Lancashire, who have won a game more, while Durham are four points behind in third.
Jennings reached his maiden double-century in the morning session, before Durham declared after passing 500.
His 416-ball stay at the crease contained 23 fours and lasted nearly 10 hours.
It gave Yorkshire a very tantalising run chase and they got off to a great start, with Lees and Lyth sharing a first-wicket century stand in 32 overs.
But McCarthy got rid of Lyth just after he had reached his half-century and Williamson followed for a golden duck.
Lyth was caught at first slip by Ben Stokes, who was on as a substitute with ECB approval as he recovers from his knee operation
Gary Ballance scored a quick-fire 32 but his dismissal saw Yorkshire slip from 149-2 to 179-5.
Tim Bresnan (27 not out) and Jack Leaning (22 not out) batted out 26 overs in a stand of 59, as both sides drew for the fifth time this season.
BBC Newcastle's Martin Emmerson:
"Durham have shown some real fighting spirit this season when the chips have been down.
"They did it to turn the game on its head and win at Warwickshire - and they fought back after a poor start in the draw at Notts.
"This time, they recovered from 105-4 in their second innings against Yorkshire to post a sizeable 507-8 declared.
"And while the eyes of the press were on Scott Borthwick ahead of his expected call-up by England, it was the now England-qualified Keaton Jennings who stole the show with a fantastic 221 not out.
"Although Durham couldn't press for the win, they gave it a great try and are still unbeaten in the Championship."
Durham and Yorkshire drew their Championship match at Chester-le-Street, as the visitors fell well short of an unlikely final-day run chase.