A wonder goal from Sam Saunders set the Daggers on their way to victory before Paul Benson and Ben Strevens completed the rout to put Still's men within three points of the play-offs with just three games remaining.
Still said: "In the second half we pushed our wide players higher up the pitch and I think that once we scored the team looked comfortable.
"The longer it went, the stronger it got and it was a fantastic result for us. This dream that we all have is continuing.
"For Dagenham & Redbridge to beat Bradford in the Football League is unbelievable and makes me so proud to be manager of this club.
"It's been a fantastic season for us and the fairytale continues."