Michael Spillane gave the Daggers the lead, but they were pegged back by Calvin Zola’s second-half goal before Agogo was given his marching orders.
Despite their midweek FA Cup exertions, the Daggers looked the better side in a scrappy first half and were given the lead in stunning fashion when Spillane curled in a superb 30-yard free-kick in the 26th minute.
The Daggers could have extended their lead as Burton struggled to come to terms with the slippery conditions. Agogo saw a 12-yard shot roll the wrong side of a post and Burton goalkeeper Ross Atkins had to keep out a Josh Scott volley.
Burton hit back to level the scores in the 53rd minute when Zola headed his eighth of the season from a Cleveland Taylor corner kick.
The Daggers were reduced to 10 men on the hour mark when Agogo was sent off for a late tackle that prompted a 20-man fracas, but the visitors defended stoutly to hang on for a point.