Surrey 464 (Smith 155, Abbott 50*, Miles 5-43) and 31 for 0 need a further 58 to beat Warwickshire 343 and 209 (Yates 52, Roach 6-46)
County champions Surrey are on the cusp of a third successive Division One victory, with Kemar Roach taking a superlative 6 for 46 to reduce Warwickshire to 209 all out in their second innings after a brilliant 155 from Jamie Smith had guided them to a 121-run halfway lead.
Surrey need just another 58 runs to complete an impressive Vitality County Championship win at the Kia Oval, openers Rory Burns and Dom Sibley taking them to 31 without loss at stumps as they chase an 89-run target.
Smith, who began day three on 98, was joined by Sean Abbott in a superb ninth wicket stand of 115 in little more than 18 overs, a county record against Warwickshire, hauling Surrey up to 464 all out from their overnight 327 for 6 in reply to Warwickshire's first innings 343.
Roach, finding conventional and reverse swing with both new and older ball, took three of the first four wickets to fall before returning later to grab three more scalps in a wonderful exhibition of controlled fast-medium bowling.
Warwickshire's hopes of fighting back to set Surrey a challenging fourth-innings target had already been dented when Abbott pulled off a stunning caught and bowled, low down from a fierce drive, to dismiss first-innings centurion Ed Barnard for 44.
Roach struck in his second over with the new ball, pinning Warwickshire captain Alex Davies leg-before for 3, and Jordan Clark produced an excellent delivery to have Will Rhodes caught behind for 21 after a second-wicket partnership of 51 with Rob Yates.
Left-hander Yates played some lovely shots in his 68-ball 52 but fell to the second ball of Roach's second spell when he aimed a pull at one that was not quite short enough for the stroke and lost his off stump. And Roach continued his familiar around-the-wicket angle to another left-hander, Dan Mousley, to have him lbw for 2 with a perfectly-pitched inswinger.
Warwickshire were rallied by a 75-run alliance for the fifth wicket between Sam Hain and Barnard, but Abbott's athleticism ended Barnard's 94-ball stay and Roach then returned for a spell at the Vauxhall End to bowl Jacob Bethell, shouldering arms, for 4.
Roach also bowled Hain for a stubborn 34 and Aamer Jamal for 1, both with inswingers of near-yorker length, and Dan Worrall polished off Warwickshire's innings by trapping Ollie Hannon-Dalby in front of his stumps. Craig Miles was unable to bat because of damaged right ankle ligaments.
Resuming with a deficit of just 16 in reply to Warwickshire's first innings of 343, Surrey soon lost Cameron Steel and Clark to a second new ball that was still only seven overs old at the start of play.
Steel chased a Jamal outswinger and edged behind to go without addition to his overnight 4, and Clark - after seeing Smith to three figures and hitting two sumptuous boundaries himself - chopped on against Hannon-Dalby.
That left Surrey 349 for 8 in the 93rd over but so well did Smith and Abbott bat that the champions did not only make sure of a third and fourth batting bonus point, they even reached a maximum five as the pair overtook the county's previous record ninth-wicket partnership against Warwickshire of 107 - scored at Edgbaston in 1926 by Douglas Jardine and Ted Brooks.
Abbott brought up the 400 by crashing Barnard high over wide midwicket for six, with a brutal swing of his bat, and there was also a classic off-driven four against Rhodes' medium pace, while Smith merely continued where he left off on Saturday evening by mixing responsible 'anchor role' defence with a stream of quality strokes.
Smith's third six, swung over midwicket off Rhodes, was a colossal blow beyond the longest boundary and he then pulled successive Barnard deliveries dismissively for fours.
Having denied Warwickshire a final bowling point, however, Smith aimed an expansive drive at Barnard and skied to deep extra cover where Davies took a fine tumbling catch to end one of the innings of the season so far.
Three balls later Worrall swished at Barnard, edged to Yates at slip and it was time for Warwickshire to face just one over of their second innings before the lunch interval - bowled by Dan Lawrence, and costing seven runs. It proved to be much tougher going against the Surrey quicks in the afternoon.
