Durham 189 (Hickey 36*, van der Merwe 4-59) and 130 for 5 (Stoneman 57) need 46 more runs to beat Somerset 184 (Wood 3-24, Rushworth 3-47) and 180 (Davies 49, van der Merwe 47, Onions 4-50)
Durham need a further 46 runs to not only defeat Somerset but to improve their chances of winning the Specsavers' County Championship after another day of extraordinary action.
However, they are making heavy weather of matters at Taunton. Chasing 176 to win, in their second innings, the visitors reached 130 for 5 at the close.
It has been a remarkable game during which Durham's seamers have taken 18 of the 20 Somerset wickets to fall and the Somerset spinners, Roelof van der Merwe and Jack Leach, have helped themselves to all but three of the 15 Durham wickets to tumble.
"It was one of those mornings where we hardly played and missed. Every good good ball got the edge," Matthew Maynard, the Somerset coach, said. "The first ball straightened on Marcus and he nicked it. One has come back to the skipper, quite sharply and then, Hildy got a good ball. They were got out by decent balls.
"However, to be still in the game tonight from 33 for 6 is a great effort from the lads and especially our low middle order.
"It has been an absorbing game of cricket. Fair play to them, they have utilised the new ball brilliantly, especially in the second innings, when we knew that if we got off to a good start we could push on. But their seamers have got a lot more out of this wicket than we thought they would."
After an opening day during which 17 wickets had fallen, the second day began with Durham resuming their first innings on 154 for 7. They lost Mark Wood and Chris Rushworth to Leach and van der Merwe respectively before Graham Onions was trapped lbw to Leach at 180 all out.
Trailing by only five, on first innings, Somerset sensed an opportunity to build a big enough lead to put serious pressure on Durham, in the game's fourth and final innings. It was not to be. They lost Marcus Trescothick, Chris Rogers and Tom Abell without scoring as Durham reduced their hosts to 0 for 3 in quick time. For Abell, it was a second first ball dismissal of the game.
James Hildreth managed 8 before he was snapped up by Onions at 21 for 4 and when Peter Trego was trapped leg before by the former England seamer, Somerset were staring down the barrel of a humiliating defeat. Unfortunately, for Somerset, it got worse before it got better, with Jim Allenby, who looked relatively comfortable in reaching 15, becoming Wood's first scalp of the day at 33 for 6.
Craig Overton and van der Merwe showed what fighting spirit can achieve - either side of lunch. The pair added 72 for the seventh wicket before van der Merwe was finally out, three short of his half century at 105 for 7.
Thirteen runs later, Overton was yorked by a decent ball from Adam Hickey and Leach followed in similar fashion, this time off the bowling of Wood.
Wicketkeeper Ryan Davies, one of the shining lights with the bat in the first innings, played with great guts and gusto and with Tim Groenewald put on 52 for the final wicket. Davies looked odds on to reach his 50 when he chipped a Hickey delivery to midwicket.
Having capitulated to the spinners in their first innings, Durham lost two early wickets to seamer Overton, at 1 for 1 and 19 for 2. Keaton Jennings departed without scoring and Scott Borthwick pulled a short ball to Hildreth at mid-on.
Michael Richardson and Mark Stoneman were separated at 88 for 3 when the former was adjudged lbw off the bowling of Jack Leach and Stoneman followed at 118 for 4 when van der Merwe found a way through his defence.
Somerset kept themselves in the hunt by taking the wicket of Gordon Muchall before the clock ticked over to six o'clock on a dramatic day.