A Darryn Stamp goal three minutes into added time gave Chester a dramatic last-gasp win as they opened up an eight-point gap at the top of the table.
The striker poked home from close range after Michael Twiss had squared the ball from the left just when it looked as though Dagenham had earned a share of the spoils.
Chester had taken the lead from the spot on 18 minutes after a well worked move was brought to a halt with Alex Smith upended by Tony Roberts.
Daryl Clare duly sent the keeper the wrong way with the resultant spot-kick.
The Daggers had gone close through Jimmy Jackson early on and had a great opportunity to draw level on the hour mark when a deep cross found Kirk Jackson at the far post, but he was a yard too slow and just failed to get a proper connection for what would have been a certain goal.
A chance to double Chester's advantage went begging a minute from the interval as a long ball sent Stamp clear, but the striker's shot, with only the keeper to beat, failed to even hit the target.
Two minutes after the restart it was Dagenham who were wasteful in front of goal as Mark Janney shot into the sidenetting.
Two chances in as many minutes saw Stamp twice off target, as first a header and then a volley ten yards from goal, went over the bar.
Chester were left rueing those missed opportunities as sub Leon Braithwaite pulled his side level with a bullet header from Chris Moore's cross.
Chester laid siege to the Dagenham goal in search of a winner and it looked as though it would not be their day as a Danny Shipp attempted clearance came back off his own bar and Ashley Vickers made a goalline clearance to deny Twiss, before Stamp had the last word.