Worcestershire’s second-wicket pair of Jake Libby and Tom Fell defied the Essex attack during an unbroken stand of 81 on the final afternoon of the LV=Insurance County Championship match at New Road.
The pair showed great concentration, and solid defence as the County looked to secure the draw after being asked to follow on 197 runs in arrears shortly before lunch.
Libby had moved onto 42 and Fell 35 out of 105-1 from 37 overs by tea.
Daryl Mitchell and Libby resumed after lunch on 6-0 after safely negotiating three overs from Sam Cook and Simon Harmer.
Mitchell picked up three boundaries in the space of two overs from Peter Siddle via an on-drive, a thick edge to third man and turning the Australian through mid-wicket.
But after making 20 out of 24, Mitchell shouldered arms to Cook and was bowled.
Fell, who hit a first-innings half-century, joined Libby, and the pair kept the probing Essex attack, most notably spinner Simon Harmer at bay.
Fell cover drove Paul Walter for four, and the 50 partnership with Libby came up from 115 balls.
Libby moved into the 40s as he cut and then drove Dan Lawrence for boundaries as the 100 came up in the 34th over.
In the morning session, Riki Wessels (33) and Ben Cox (37) extended their sixth-wicket stand to 54 before both were dismissed by Sam Cook, who picked up three wickets in 16 balls.
But the last wicket pair of Dillon Pennington (30) and Charlie Morris provided stubborn resistance in adding 38 from 15 overs before Worcestershire were dismissed for 364 in 138.1 overs.