Promotion-chasing Dagenham & Redbridge had looked to have secured the points after racing into a two-goal lead, but the home side hit back late on through David Mannix and Kevin Roberts.
The visitors opened the scoring in the sixth minute when Jon Nurse pulled the ball across the face of goal for Ben Strevens to sidefoot home from ten yards out.
On 26 minutes, goalscorer Strevens wasted a great opportunity to put his side two up, when a header from Matt Ritchie sent him clean through on goal, but his finish struck the post and rebounded to safety.
Ritchie had the ball in the net on 33 minutes, only for his effort to be ruled offside, but he did not have long to wait as three minutes later he doubled the advantage.
Chester defender James Vaughan cleared the ball straight to Ritchie, who lashed home with a thunderous left-foot effort from just inside the penalty area.
The second half brought the expected response from the home side, who had clearly had a severe talking-to at half-time from manager Mark Wright.
Lawrence Wilson shot wide and Kevin Ellison fired an effort on the turn over the bar.
The last few minutes saw the game turned on its head when Mannix gave Chester hope with a header from Ryan Lowe's corner on 86 minutes.
Three minutes later Lowe again turned provider, his free-kick finding Roberts, who headed home from close range to steal a point.