The Portsmouth man bagged his fifth goal of the season 19 minutes from time, but City could have been out of sight by then if they had made the most of the chances that came their way.
The Daggers dominated play for large periods without really testing City keeper Rhys Evans and the Bantams should have been ahead by the break.
On-loan Burnley winger Steve Jones fired over from six yards when he looked set to open his City account and Bradford's leading scorer, Peter Thorne, missed an even better chance soon after when he fired wide at the far post.
City looked dangerous on the counter attack and when Michael Boulding raced clear after 27 minutes he should have done better when he pulled his shot wide of the mark.
Evans did well to block at the feet of Paul Benson after a mistake by Graeme Lee and just before the interval he reacted smartly to deny Magnus Okuonghae's close-range shot.
Dagenham started the second half on the front foot, but they had a lucky escape when Nicky Law's long-range strike rattled the bar after 58 minutes.
Four minutes later City stunned the visitors with another excellent counter-attack.
Law's surging run down the right stretched the Daggers defence and Boulding guided his well-driven cross beyond Tony Roberts with a superb volley from 14 yards.
Two minutes later Roberts did well to stop a snap shot from Lee and when the rebound fell to Jones he again fired wide from close range.
Daggers striker Ben Strevens caused City's backline problems throughout and with 19 minutes left he pulled the ball back from the deep in the Bradford box and when Evans parried the bal into the path of Ritchie, he drilled his shot past the keeper from close to the penalty spot.
Dagenham were fuming late on when skipper Mark Arber went over in the Bradford box, but despite the protests referee Stuart Attwell waived away their strong penalty appeal.