Phil Mustard and Liam Plunkett both hit half-centuries to earn Durham a draw and extend Yorkshire's winless run in first-class cricket to 19 games.
After Durham resumed on 288-7, Mustard (85) and Plunkett (65) shared 147 for the eighth-wicket to help the visitors declare their second innings on 421-9.
Chasing 287 to win, Yorkshire reached 98-4 when a draw was agreed.
Unbeaten Durham remain top of Division One, while Yorkshire are without a Championship win since June 2008.
Beginning the day 153 runs behind and needing quick wickets to have any hope of forcing victory, Yorkshire were made to pay for dropping Mustard twice in the morning session.
The wicketkeeper was put down on 55 at slip by Jacques Rudolph off the bowling of Tim Bresnan and was then dropped by Adam Lyth at mid-on from a delivery by Adil Rashid.
When Mustard was eventually caught and bowled by Bresnan it ended Durham's highest ever eighth-wicket stand against Yorkshire and when Plunkett was caught by Hoggard off Rana Naved ul-Hasan it signalled the Durham declaration.
Plunkett and Ian Blackwell then each picked up two wickets to reduce the home side to 68-4, but Andrew Gale and Jonathan Bairstow combined to calm Yorkshire nerves and see them to a draw.
On the day that he was recalled to the England squad for the second Test against Australia, Steve Harmison bowled 11 overs without success.
Durham coach Geoff Cook told BBC Radio Newcastle:
"We've had a good first half of the season and played some good cricket.
"We probably didn't apply ourselves as we would have liked on the first day but we stuck with the task and did well in the second innings.
"It was a slow wicket where a lot of application was needed and they batted pretty well, but we saved the game and then had a chance of winning it."
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