Rashid stars for Yorkshire
Adil Rashid enjoyed his best bowling figures at Headingley in four years to keep Yorkshire in with a good chance of beating Durham and taking a clear lead in the LV= County Championship Division One table.
The leg-spinner captured four for 73 as Durham were forced to follow on after being bowled out for 231 - trailing by 195 runs - as they closed the third day on 59 for one, still 136 adrift.
The eight bonus points which Yorkshire have taken from the match mean they currently share top place with Nottinghamshire.
Durham resumed their first innings in the morning on 50 for one and with plenty of bowling ahead of them if they were to go on and win the match.
Yorkshire were eager for early wickets. One came quickly when Ryan Sidebottom managed late movement off a perfect length to Scott Borthwick who edged into Jonny Bairstow's gloves.
Opener Keaton Jennings settled in solidly, however, and was well supported by Michael Richardson, the former taking two off-side boundaries in an over off Jack Brooks before greeting the arrival of Rashid into the attack with a swept four.
Jennings advanced with some clean drives to his half-century off 122 balls with eight fours but having reached 56 he pushed at the accurate and miserly Steven Patterson and Adam Lyth scooped up the catch at second slip.
In the next over, Gordon Muchall (five) was lbw on the back foot to Tim Bresnan and it rapidly became Yorkshire's morning as Richardson (23) chipped back the last ball before lunch to Rashid, Durham having slid to 119 for five with three wickets toppling for nine runs.
Soon after the interval, Yorkshire had two chances on 131 to make life easier for themselves but were unable to take either of them.
Phil Mustard edged Brooks to Alex Lees at third slip but be could not grasp a sharp chance and Paul Collingwood would have been run out off the next ball if Sidebottom had scored a direct hit on the stumps.
On at least two occasions, Sidebottom pleaded in vain to umpire Richard Illingworth for lbw decisions against Mustard but it was Rashid who went on to break the troublesome 51 stand by having Mustard snapped up at short leg by Jack Leaning for 17.
Rashid was looking more confident than he had done for some time and - after John Hastings had looped a catch to Lyth at slip - he made Phil Coughlin (11) pay for on-driving him for six to get off the mark by enticing him to hit straight into the hands of Brooks at deep mid-on.
Collingwood remained a threat to Yorkshire's ambitions, completing his 50 off 89 balls with five fours, and when he received a beamer from Brooks the bowler was given an official warning.
Patterson took the new ball for the second delivery after tea and he shared it for an over with Rashid before pinning Mark Wood (13) lbw.
Sidebottom replaced the spinner and his first ball had Chris Rushworth lbw, Collingwood remaining unbeaten on a defiant 64 from 106 balls with six fours.
Both Sidebottom and Patterson were the models of consistency throughout the innings, Patterson's two wickets costing him 27 runs off 20 overs and Sidebottom being similarly rewarded from 14.2 overs with six maidens.
But the happiest man was probably Rashid whose figures were his best at Headingley since picking up five for 137 against Warwickshire almost exactly four years ago and his best in any match since taking five for 78 against Middlesex at Lord's last summer.
All out for 231 and following on with 26 overs of the day still remaining, Durham were given a mainly untroubled start by Mark Stoneman and Jennings and at 33 for no loss, after 14 overs Rashid was brought on from the football end.
But he was given only two overs by skipper, Andrew Gale, who then turned to the off-spin of Lyth and it proved to be an inspired move because he clean bowled Jennings with his fifth delivery and Durham were 39 for one.
Borthwick then helped Stoneman to see it through to the close without further mishap.