Earlier, Sussex had done well before lunch to remove three players capable of taking the game away from them quickly.
Ollie Pope signalled his intentions by hitting four boundaries in Fynn Hudson-Prentice’s opening over only to waste a good start when he was caught at second slip trying to guide the ball down to third man.
Lawrence was held at long on and Smith at long off but there was no dislodging Sibley, who passed 10,000 first-class runs on 123 when he took a boundary off Henry Crocombe before hoisting Jack Carson down the ground for six to ease Surrey past Sussex’s 358.
Another six off Carson took him to 150 and he seemed to be cruising towards a double hundred when he tried to belt Carson over the top again and was beaten in the flight to end a vigil that had lasted more than eight-and-a-half hours.
Sibley has now faced a staggering 888 balls in six innings this season, batting for more than 20 hours – after he was last summer’s leading Division One run-scorer with 1,274 runs.
When Haines pinned Clark Surrey’s lead was 103 but, just as Sussex’s had on day one, Surrey’s tailed wagged vigorously.
With Thomas now into his stride, at the other end Sean Abbott took his cue and they added 161 in 27 overs, a new eighth-wicket Surrey record in this fixture beating the 150 by Robin Jackman and Intikhab Alam at The Oval in 1973.
Abbott (76) was caught at backward point as Sussex took the last three wickets in four balls, but it was a brief respite after 159 draining overs in the field.