After the London side opted to declare their overnight score of 428 for five, which meant Sam Robson was unbeaten on 215, the Division One defending champions moved to 83 for one at lunch on day three.
William Porterfield was the only wicket to go down as the left-hander was snared by Corey Collymore for 20, with Laurie Evans and Jonathan Trott making unbeaten scores of 37 and 25 respectively and leave their side 345 runs adrift.
Callum Thorp removed both Surrey openers as Durham got off to a decent start despite losing the toss at The Oval. After play was delayed by rain, Thorp made up for lost time on his return to the side, first having Rory Burns caught behind before dismissing Jason Roy.
Arun Harinath and Vikram Solanki guided Gareth Batty's side to 55 for two after 15 overs.
There was no play possible before lunch at Headingley, with the match into its final day.
Somerset will look to resume on 190 for five in their first innings in response to Yorkshire's 505 for nine declared, and only a collapse of epic proportions would signal anything other than a draw.
- Sports & Recreation
- Jonathan Trott
- William Porterfield
- Sam Robson
- Corey Collymore
- Callum Thorp