And Chichester, who suffered a 1-0 defeat in the reverse fixture at the turn of the year, had keeper Kieran Magee to thank for a string of outstanding second half saves, including one from the penalty spot in the 85th minute.
Clear cut chances were few and far between in a goalless opening 45 the visitors edged.
Jamie Horncastle returned to partner Ben Pashley at the heart of the defence in a starting XI otherwise unchanged from the one that lost late on away at Herne Bay.
EG right back Fintan Walsh’s long throw into the box with barely 60 seconds on the clock was cleared by Emmett Dunn before Magee got to the ball ahead of Ben Aubrey when it was recycled.
Horncastle climbed well to nod a couple of headers away moments later and Ben Mendoza tidied up after conceding a free-kick on three minutes.
Pashley’s set-piece at the other end was just too strong for Ethan Prichard, as was Kaleem Haitham’s pass to the Chi No7.
Ryan Davidson then broke two tackles driving into the penalty area before both sides gave away a series of niggling fouls.
Slick skill by Prichard opened things up and the referee quite rightly pulled play back for a free-kick as Prichard was blocked.
Next, nice feet from Tyrone Madhani teed up a rare Chi opportunity but his effort didn’t really test keeper Luke Glover.
Rob Hutchings then fed an inviting pass down the left flank towards Madhani but it rolled out for a goal kick.
Tariq Straker picked Davidson’s pocket and raced forward to find Aubrey whose cross nicked off a defender and into Magee’s arms.
Straker was at it again as the Wasps pressed once more but Max Walsh headed his delivery over the bar.
Chi countered through Prichard and his pace drew a foul off Miles Cornwell who somehow escaped a caution from referee James Robinson.
Composure by Pashley allowed him to deal with a bit of danger on the half hour and then Davidson cleared Aubrey’s cross.
The home side won a corner only for Horncastle’s shot to be hacked away before Pashley did well up against Aubrey.
Madhani and Haitham combined only for the move to fizzle out and Walsh whipped one in that Davidson steered out for a corner.
Kie Douglas hit this deep. Dunn missed it and Straker’s lofted pass was just too long for Cornwell.
Tom Summerfield was the first player into Mr Robinson’s notepad for a foul on Dunn five minutes before the break and then the Canadian blasted an effort into an opponent.
And on the stroke of half time Dan Uchechi’s free kick was headed into Magee’s gloves by Glenn Wilson.
All the drama came in the second period.
Haitham fizzed a shot off Straker for a corner early-doors.
Clack then found Hutchings with a lovely ball the No3 couldn’t quite get under control before Cornwell pulled a fine stop out of Magee.
Cornwell had another go on 57 minutes only for his fierce attempt to cannon off a teammate.
Next, a poor Davidson back pass presented Aubrey with a chance he couldn’t capitalise on and intelligent defending by Horncastle denied Walsh after a turn of pace.
Haitham lost his footing following a neat exchange between Hutchings and Clack.
Aubrey got a talking to from the ref and the visitors brought Drew Cooney on for Summerfield.
Another bit of vision from Clack set Prichard up who needed to make a better connection.
Cooney then might have broken the deadlock but Magee tipped his cracking drive spectacularly round an upright.
Chi coped with the subsequent corner and one on the other side before Charlie Oakwell-Boulton replaced Horncastle.
There was euphoria for the travelling fans behind the Archery End when a fantastic volley from Cornwell outside the box found the back of the net on 69 minutes.
East Grinstead ramped it up and Oakwell-Boulton was forced into a couple of blocks.
The Chi back-line hooked clear a Uchechi corner before Haitham thundered an effort against a post against the run of play.
Cooney picked up a booking with 15 to go and Omar Folkes replaced Douglas as EG rang further changes.
The sub struck an 81st minute free-kick straight at Magee.
Davidson then gave the ball up cheaply to Cooney who was offside anyway before Pashley brought Folkes down in the penalty area in the 85th minute.
Magee kept Chi in the game once more though with a brilliant save to deny Cornwell from the spot.
Aubrey was then cautioned with a couple of minutes of normal time remaining and made way for Adetokunbo Zambara.
Walsh lifted an effort onto the roof of the net before on 92 minutes, with seemingly a fourth consecutive league loss without scoring on the cards, Chi countered, Hutchings squared the ball and Clack drilled it home for a share of the spoils.
Chichester remain 11th and travel to Burgess Hill Town on Bank Holiday Monday 18th April (Kick Off 3pm) for their penultimate match before welcoming Ramsgate to Oaklands Park on Saturday 23rd April (Kick Off 3pm).
Chichester – Magee, Davidson, Hutchings, Dunn, Horncastle, Pashley, Prichard, Mendoza, Clack, Madhani, Haitham. Subs: (Wallis, Oakwell-Boulton, Farrier, Overton)