Blundell's penalty was his first goal for Chester since his return this summer
Chester City had to come from behind with a disputed penalty to claim a third draw in four away league games on their first-ever trip to Eastbourne.
Eastbourne led inside five minutes when Andy Atkin took advantage of Kevin Roberts' poor headed back-pass.
But Chester levelled in first-half injury time from the spot, Gregg Blundell slotting home after Matt Crabb's challenge on Neil Ashton.
Two Eastbourne players were booked protesting about the decision.
Chester keeper John Danby made two important first-half saves to deny Liam Enver-Marum and Simon Weatherstone. And Atkin wasted the best chance to win when he hit the post from 12 yards with 10 minutes left.
But City also had a great chance before the break, Nick Chadwick being denied by home keeper Michael Jordan.
Bottom club Chester remain 26 points adrift of safety going into Tuesday night's rearranged home game against Gateshead (15 September, 1945 BST).
Eastbourne Borough: Jordan, Jenkins, Pullan, Elphick, Brown, Armstrong (Baker 75), Enver-Marum (Smith 63), M Crabb, Weatherstone, Atkin, N Crabb. Subs Not Used: Knowles, Smart, Johnson
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.