Essex 162 and 224 for 4 (Cox 77*, Critchley 46*) need another 106 runs to beat Warwickshire 397 and 94 (Yates 28, Critchley 4-24, Harmer 3-28)
An unbroken fifth-wicket century stand between Jordan Cox and Matt Critchley gave Essex the chance of pulling off an unlikely Vitality County Championship victory over Warwickshire at Chelmsford.
Set 330 to win in 170 overs, Essex finished day three on 224, requiring a further 106 runs on the final day, with six wickets standing, to resurrect their hopes of launching a serious challenge to Surrey at the top of the table.
Both players mixed aggression with caution as they pieced together a partnership worth 112 in 37 overs with Cox becoming only the third player in the match to pass fifty. He was 77 not from 144 balls at the close with Critchley on 46 from 111.
Warwickshire, who had amassed 397 in the first innings and looked favourites to record their first win of the season, were dismissed inside 38 overs for just 94 in their second. Essex spinners Critchley and Simon Harmer sharing seven wickets, including all five that fell in the morning.
Essex's chase had begun disastrously when Feroze Khushi was trapped first ball on his crease playing down the wrong line to Michael Rae.
It became even worse when Che Simmons pulled off a stunning diving catch in the covers to account for Nick Browne. The batsman dwelt momentarily before walking ahead of the result of the umpires' consultation and receiving a consolation pat on the back for his honesty.
Essex consolidated either side of lunch as Elgar and Westley stood firm. Westley, dropped on three whipping the ball off his legs to midwicket, hooked Simmons's short balls and defended resolutely as Rob Yates mixed up his lengths.
Elgar found a gap through the covers for the boundary that brought up only the second fifty partnership in the match - the first was ultimately worth 209 between Ed Barnard and Michael Burgess. Almost immediately, though, Simmons produced a fuller ball and Westley departed lbw for a 69-ball 18.
The introduction of Cox upped the tempo and the fourth-wicket pair put on 47 in 12 overs as Warwickshire rang the changes until Barnard found one that kept low and pinned Elgar for 60 from 85 balls.
The third half-century stand was brought up by Critchley's lofted four off Yates. Critchley had taken time to get started but he hit full throttle when he launched Yates for six over long-on. Cox was setting the pace, though, and reached his fourth score of fifty-plus from 101 balls.
Warwickshire had opted not to enforce the follow-on despite being 235 runs ahead on first innings. Their second innings lasted just another 75 minutes in the morning session while they added 51 runs for five wickets.
Rae's nightwatchman duties did not extend long before he was beaten by the extravagant turn of Harmer, became unbalanced and was bowled. It was Harmer's second wicket in five balls, separated by a night's sleep.
Burgess, one of two Warwickshire centurions in the first innings, lasted 35 balls this time for 18 before he pulled Critchley to midwicket where Luc Benkensein - who had only just entered the field as a substitute ahead of that ball - took a comfortable catch.
Chris Benjamin, called down from Edgbaston as concussion substitute for Sam Hain who was struck on the helmet at short leg by Jordan Cox on day two, faced seven balls before he nicked to none other than Jordan Cox at slip.
Jacob Bethell hit Critchley's first two balls of an over for a towering straight six and an off-driven four. But he skied the third ball and Critchley had time to move to mid-off to claim the caught-and-bowled in figures of 4-24.
Harmer (3 for 28) wrapped up the innings when Simmons charged down the wicket and picked out Westley stationed on the long-on fence.
