The Daggers staged a barnstorming finish to keep their promotion push on track with a fourth successive victory.
But they left it mighty late, with substitute Jordan Maguire-Drew grabbing the winner in the 96th minute.
The extra time was added because of blatant time wasting by Chester, who ultimately paid a heavy price for it.
Confidence was high among the fans before the game following last week's great win at Tranmere.
But for a long time it seemed like a case of 'after the Lord Mayor's Show' as the Daggers were below their best. Their passing was not crisp and they lacked a cutting edge.
They wasted a glorious chance after only six minutes when they were awarded a penalty after Fejiri Okenabirhie was upended in the box. But leading scorer Oliver Hawkins saw his spot kick saved by Chester keeper Liam Roberts.
Daggers keeper Elliot Justham did well to turn a fierce shot from Elliott Durell over the bar before the Daggers made the breakthrough on the stroke of half time.
Full back Jake Sheppard hit the jackpot with a well struck left footer after a throw in was cleared to him.
A mistake by Hawkins allowed Luke George to equalise in the 51st minute. Oliver let the ball run past him, convinced it was going out of play. But Chester kept it in and scooped it into the goalmouth for George to finish.
More slack defending gave the visitors the lead seven minutes later. They made tracks down the right and put the ball in for Tom Shaw to slam home.
To their credit the Daggers kept plugging away and they got back on terms when Corey Whitely put away a second penalty in the 85th minute. That was awarded after Johnny Hunt handled the ball on the goal line and was sent off.
Minutes later Chester got away with what looked like a handball in the box that should have given them a third penalty. But referee Alan Young let that one go.
But Chester were not off the hook as the Daggers looked for a winner and with only seconds left Maguire-Drew won it by pouncing to fire home after a Paul Benson header came back off the bar.
Attendance: 1250 (161 away fans)
Daggers: Justham, Widdowson, Robson, Raymond (Howell, 61 mins), Guttridge(Maguire-Drew, 61 mins), Okenabihrie (Benson, 76 mins), Hawkins, Boucaud, Whitely, Donnellan, Sheppard
Chester: Roberts, Vassell, Hudson, Astles, Hunt, Durrell (O'Brien, 90+6 mins), Shaw, George, Joyce, Horwood (Hughes, 75 mins), Alabi