Opener Graeme Smith missed the chance to wrestle control against Essex at the Kia Oval, falling three short of a new LV= County Championship personal-best for Surrey.
Captain Smith hit 65 as Surrey replied with 217 for six to Essex's 306 all out on day three of the Division Two clash.
The former Proteas skipper was unable to turn his half-century into a match-defining knock though, leaving Surrey frustrated in a contest almost certainly heading for a draw.
Matt Dunn claimed his second championship five-wicket haul as Essex added just 81 to their overnight total.
Surrey were forced to endure a nervy final session, slipping from 111 for one at tea to 165 for five in a troublesome 20-over spell.
England spinner Monty Panesar returned solid figures of 2-43 from 18 overs, while Tymal Mills also took two wickets, but Surrey will bemoan leaking five wickets for 106 runs in the day's final session.
England Under-19 cap Dunn became the first Surrey bowler in 56 years to take five wickets on his championship debut in a June 2011 victory at Derbyshire.
The Egham-born seamer has had to wait patiently for chances since, with this Essex clash just his fifth championship appearance.
Surrey bowling coach Stuart Barnes believes this campaign could yield a breakthrough for Dunn, and the pace bowler has quickly indicated form vindicating that faith.
Big-hitting New Zealand batsman Jesse Ryder sealed his deal to join Essex for the rest of the season in mid-morning, but news of the Kiwi's arrival failed to inject life into the Chelmsford club's innings.
James Foster was the first wicket of the day, falling for 20 off Stuart Meaker with Jason Roy holding on at third slip, after Foster had been put down at second in the same over.
David Masters racked up 23 as Essex fought to accelerate proceedings, only to be caught at mid-off by Dunn off Chris Tremlett.
Napier's measured 28 was Essex's last anchoring effort, but he was caught at first slip by Smith, leaving the visitors 279 for nine.
Panesar was the last to depart when removed on 17 - but not before a stunning drive off Tremlett - as Dunn completed his five-wicket raid.
Rory Burns had seen off the new ball to ease Surrey into their innings, only to perish to some quick-thinking from Bopara for 17.
Bopara picked up the ball and flicked them at the stumps on his follow-through and his direct-hit accounted for Burns, who had been sent back to his crease by Smith having set off for a quick single.
Former Proteas skipper Smith restored calm, unruffled as he stroked the first half-century of the match from 66 balls.
— Surrey Cricket (@surreycricket) April 22, 2014
Surrey reached tea at 111 for one from 30 overs, with Smith on 58 and Dominic Sibley 20.
Smith's defiant knock came to an abrupt end in the evening session, however, as he was caught out by extra bounce from David Masters.
Jaik Mickleburgh held the catch at third slip to send the 33-year-old back to the pavilion after a 77-run stand.
Sibley whacked Panesar for two fours from one over en route to 34, only to edge Mills into the slip cordon, with Mickleburgh producing a fine full-stretch catch.
That setback put Surrey on 156 for three, before bad light threatened play.
Gary Wilson then holed out cheaply to Napier off Panesar and Steven Davies lasted just 17 minutes as Surrey's middle-order travails continued with Mills striking again.
Panesar bowled Meaker around his legs as Zafar Ansari was pushed down the order after his concussion after colliding with the boundary fence yesterday ruled him out of day-three action.
Chris Tremlett was therefore sent out and he remained unbeaten alongside Roy, who was 30 not out by the close.