Jack Leaning and Tim Bresnan survived for 25 overs after coming together when off-spinner Ryan Pringle ended any lingering chance of a late onslaught by removing Andrew Gale and Alex Lees in successive overs.
Lees played fluently in an opening stand of 112 with Adam Lyth, which suggested the target was reachable. But he went into his shell after two wickets fell in two balls during an excellent mid-afternoon spell by Irish seamer Barry McCarthy.
Lyth departed reluctantly for 50, apparently believing he had played a yorker length ball into the ground before it flew at just above head height to first slip.
The catcher was Ben Stokes, on as a substitute with ECB approval as he recovers from his knee operation. He replaced Paul Collingwood, who has a fractured thumb.
Replays suggested Lyth’s dismissal was fair and there were no doubts about the next ball, which nipped back sharply to have Kane Williamson lbw.
From the hat-trick ball Gary Ballance survived raucous appeals for a leg-side catch by Michael Richardson then scored 17 off the next six balls he faced.
But Durham recalled Graham Onions, who in his first two spells conceded only 20 in 11 overs and had Ballance caught behind for 32 with an excellent ball from round the wicket. It pitched on off stump and seamed away to take the edge.
Gale made a sedate 17 before he edged behind when pushing forward, then Lees stayed back and was bowled by a shooter for 74.
Durham batted on for 55 minutes to add 55 runs in the morning, Keaton Jennings moving on from 185 to 221 not out, the fifth highest score by a Durham batsman.
The 23-year-old left-hander had batted for 578 minutes, faced 416 balls and hit 23 fours when the declaration came on 507 for eight, Durham’s highest second innings total.
Yorkshire captain Andrew Gale said: “We didn’t really talk about going for the runs. But we knew if we could get to tea in a good position, like we did at Trent Bridge, we might have had a go.
“But this was a different pitch with the ball going up and down and it was turning quite a bit towards the end.
“In the end we will take a draw. We didn’t throw away our good position after day two – they fought back really hard and Jennings played an outstanding innings, showing a lot of grit and determination.”
Keaton Jennings said: “I’m very proud and happy to have come out of the game with a personal milestone and with a draw considering the position we were in after day two.
“We did well to get out of a hole and we could have gone on to win with a bit more luck. It shows the character of the side in trying to win from a dead position.”