Jeffers' header in the final minute of injury time salvaged a point for the Clarets who looked like they were going to suffer their first defeat in six.
Despite having been under the cosh for most of the first half the Rocks took a surprise lead when Chris Bush’s back pass was latched onto by Reece Harris who rounded Ross Fitzsimons to open the scoring.
The Clarets rallied and went into the break on top as Anthony Church scored his first goal since returning the Club on the stroke of half time after the ball fell to him from a corner.
City started the second half well and had a couple of half chances but they were made to pay for another defensive error by Bush who lost the ball in a dangerous area. Harris sprinted clear to force a good save from Fitzsimons but Joe Gardner headed in the rebound.
Chelmsford had a goal disallowed in both halves and continued to press for an equaliser to preserve their unbeaten run with Jeffers rising high to head home at the death to win City a point.
The draw ends a run of five straight wins for the Clarets that put them just three points off the top of the National League South table, and Rod Stringer’s warnings to his side about them being punished for not taking their chances finally bared fruit.
The Clarets started much the brighter of the two sides and came close twice through Billy Bricknell who first poked the ball just wide after getting on the end of a Shamir Mullings flick on before having a goal ruled out for offside.
Chelmsford City though failed to make their early pressure pay as the visitors took the lead completely against the run of play through Reece Harris. Chris Bush appeared to be having his shorts pulled by Harris which went unseen by referee Paul Kelly. Bush tried playing the ball back to Ross Fitzsimons but Harris read what the Clarets centre half was going to do and ran straight onto the back pass, calmly rounding Fitzsimons to open the scoring for the away side.
Rod Stringer’s side looked rattled by the goal with both Bush and Mark Haines going into the book for dissent, but the Clarets soon settled back into the their rhythm and saw Josh Rees’ first time strike get cleared off the line.
City continued to press for an equaliser before half time and Anthony Church had a great chance when he was picked out by a low cross from Bush but the Clarets captain couldn’t get dig the ball out from underneath him before it was cleared.
Bricknell forced Lidakevicius into tipping his volley over the bar late in the half as the Rocks stood firm but they weren’t able to hold out until the interval as the Clarets equalised in the 44th minute.
A long throw from Bush was headed out and recycled by Bagasan Graham. His hooked cross towards the far post was headed back across goal by Mullings and after bobbling around in the area Anthony Church was on hand to smash it into the bottom corner to level.
John Coventry made a double substitution at half time bringing on Teddy Nesbitt and James Walker for Michael Freiter and Harry Honesty and immediately had a chance to go back in front through Kane Ferdinand who headed wide from a corner.
Bricknell had half the ground cheering as they thought his effort on the turn had crept in when it had hit the side netting, and the striker felt he had a good claim handball and a penalty when his header was blocked away for a corner.
The Clarets though were the makers of their own downfall as a second defensive lapse from Bush resulted in a second East Thurrock goal. Bush tried to play the ball out from the back and was robbed by Harris. His strike was well saved by Fitzsimons but there was nothing the City 'keeper could do about Joe Gardner’s header on the rebound as the Rocks went 2-1 ahead.
City had been punished by two lapses in concentration and Stringer reacted to going behind again by replacing Daniel Blanchett with Shaun Jeffers to go three at the back, the formation that had served the Clarets well in their previous two games.
Jeffers was in the thick of it straight away as the ball fell to him at the far post from a corner but he wasn’t able to bundle the ball in. East Thurrock immediately counter attacked and could have put the game to bed through James Walker who couldn’t lift the ball over the advancing Fitzsimons.
Phil Walsh – a former striker turned centre back – was thrown on in the final 10 minutes as Chelmsford kept knocking at the door of their visitors with Jeffers having an effort cleared off the line.
East Thurrock were dealing with the Bush long throw with ease late on as Chelmsford threw everything they could in search of an equaliser with Jeffers having a glorious chance late on, but he wasn't able to get enough on his header to beat Lidakevicuis.
But there was more than enough on his header in the 94th minute as Jeffers rose highest to rocket Luke Daley's cross beyond Lidakevicius to leave both sides with a point.
1. Ross Fitzsimons
2. Ashley Miller
3. Daniel Blanchett
4. Josh Rees
5. Chris Bush
6. Mark Haines
7. Luke Daley
8. Anthony Church (C)
9. Shamir Mullings
10. Billy Bricknell
11. Bagasan Graham
12. Phil Walsh (On for Ashley Miller 80’)
14. Shaun Jeffers (On for Daniel Blanchett 60’)
15. Frankie Merrifield (On for Josh Rees 87')
16. Corby Moore
19. Sheldon Sellears
East Thurrock United:
1. Lukas Lidakevicius
2. Ryan Sammons
3. Michael Clark
4. Ben Wood
5. Joe Ellul
6. Kane Ferdinand
7. Reece Harris
8. Michael Freiter
9. Harry Honesty
10. Joe Gardiner
11. Tom Wraight
12. Ben Marlow
14. Teddy Nesbitt (On for Michael Freiter 46’)
15. James Walker (On for Harry Honesty 46’)
16. Jamie Age
Chelmsford City: Anthony Church (44’), Shaun Jeffers (90+4')
East Thurrock United: Reece Harris (23’), Joe Gardner (57’)
Chelmsford City: Chris Bush (Dissent – 23’), Mark Haines (Dissent 25’), Shamir Mullings (Foul 90+1')
East Thurrock United: Joe Ellul (Foul – 51’), Ryan Sammons (Foul 83’)
Referee: Paul Kelly
Assistant Referees: Thomas Marshall & Andrew Loe
City Man of the Match: Anthony Church