Durham were 98-4, 276 ahead, when Muchall was caught behind off Ashraf for 19 in the 36th over.
Ian Blackwell added 14, before nicking the ball to Adam Lyth in the slips off Richard Pyrah, as Durham stood at 124-5 in the 44th over.
Benkenstein had to dig in and he struck a patient fifty, from 103 deliveries including six fours. At lunch Durham were leading by 338, at 158-5 with Benkenstein 53* and Richardson 18*.
During the afternoon session Michael Richardson became the first Durham debutant to score fifty in both innings since Michael Di Venuto in 2007, having faced 104 balls and hitting five fours.
Benkenstein scored his second century in as many matches shortly after , off 173 balls including five boundaries , giving Durham a lead of 424.
The pair didn’t look troubled by the Yorkshire attack and accelerated their run scoring, passing the hundred partnership, with some aggressive hitting.
Benkenstein passed the 150 mark in the 87th over (off 212 balls including 17 fours and a six) but was out next ball when he was caught at deep mid wicket by Lyth off Patterson. His dismissal signalled the Durham declaration with their total at 311-6, Richardson 73*, having established a lead of 489.
The opening Yorkshire pair put on 64 before Lyth was caught behind off Callum Thorp for 26 in the 17th over. Root and McGrath found runs difficult to come by, scoring slowly, and with McGrath crowded by fielders he eventually succumbed and edged a Blackwell delivery to Di Venuto in the slips, scoring just seven runs off 30 deliveries, having taken 21 balls to get off the mark.
At the end of day three Yorkshire were 88-2, trailing by 401, with Root 38* and Gale 3*.
Durhamccc.co.uk spoke to Dale Benkenstein at the close of play, “I think it’s always just nice to have time in the middle and if you can make that into hundreds that’s even better. I’ve been determined to play better than last year as it wasn’t up to my standards so this has been a good start.
“There’s still something there in the pitch, it’s not by any means a bad wicket, but there’s a bit of spin and every now and then the ball is seaming about a little bit, with some inconsistent bounce, but it keeps you honest as a batter. If we can get a few wickets quickly, the whole game could be under pressure.
“We’ve bowled 32 over tonight and hot another 96 tomorrow so if we can’t bowl a side out in that time you’re probably not going to bowl then out anyway. You don’t want to dangle the carrot too much because then you have to start defending, it’s better to just attack. It gives Scott Borthwick a real good chance to come into the game, as a leggie, where you’re not bothered about going for runs.”
Follow the action from the day, as it happened on Live Match Chat (www.durhamccc.co.uk/live-match-chat) Highlights of Saturday’s play will be uploaded on Sunday at www.durhamccc.co.uk/durhamtv/highlights