JASON Roy was four short of his second century of the match at tea, when Surrey were 168 for four, needing a further 113.
After his first innings stand of 164 with Zafar Ansari the pair put on 143 after coming together at 11 for three.
Durham had to turn to Scott Borthwick and in his second over he turned one sharply into left-hander Ansari to have him lbw on the back foot for 51.
Both batsmen needed treatment for hand injuries, which was slightly worrying for them ahead of Saturday's Royal London Cup final.
Roy was struck by Brydon Carse on 44 but then hooked the paceman to fine leg for one of the nine fours in his 79-ball half-century.
On 65 he inside-edged Mark Wood just past his leg stump for four, but with the pitch offering little under a cloudless sky he looked more secure than in the first innings and played an array of powerful shots.
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