Graham Onions opens the bowling on day two which sees Nick Compton running two to reach 150. Callum Thorp struck with his first ball when Butler was caught behind for 9.
Somerset gain maximum batting points passing 400 in the sixth over of the day.
Compton and Peter Trego weren’t especially troubled , despite the former ducked into an Onions delivery in the 105th over (8 overs into the day) when he was on 159 but after receiving attention from the physio continued his form in the middle.
Durham required the assistance of 12th man, Keaton Jennings, early on after Ian Blackwell, who was on and off during the first session, was unable to field after suffering back spasms.
Trego brought up his fifty (52 balls, seven fours and a six) and the 150 stand shortly with 30 minutes to go until lunch.
A short rain delay halted play for a few minutes, just after Compton had reached 200, smashing a Scott Borthwick full toss for four, from 356 balls including 21 boundaries.
At the lunch break the visitors were 515-5 with Compton 214* and Trego 61*.
Scott Borthwick prevented Trego from becoming the third centurian of the Somerset innings after he was trapped lbw on 98 with the Somerset total at 578.
Compton passed the 250 mark and went on to push Somerset over 600 with the visitors declaring on 610-6, the highest total posted by visitors to Emirates Durham ICG.
Durham started well and were 52-0 at tea with Michael Di Venuto going on to pass the fifty mark for the 32nd time for his county, from 77 balls including seven fours, after the break.
Will Smith (13) fell shortly after, caught by Trego becoming Steve Kirby’s first scalp of the match and his replacement, Gordon Muchall fell to the same bowler, without scoring, an over later when he was caught by Hildreth leaving Durham 71-2 after 25 overs.
Durham were 123-2 after Hildreth picked up a second catch, this time off the bowling of Hussain, to dismiss Stokes for 21 with 16 overs remaining.
Gregory claimed the scalp of Di Venuto (86) after he was caught by Compton with 11 overs to go and Durham 139-4, trailing by 471.
Dale Benkenstein (26) and Phil Mustard (19) steered Durham through to the close with the Durham total at 182-4, trailing by 428.