Former Daggers striker Michael Cheek sent his old club to a third successive defeat in the National League at Hayes Lane on Saturday.
Having lost to Hartlepool and Aldershot over the Easter weekend, Daggers saw Will Wright's early free-kick comfortably saved by Mark Cousins on three minutes, before Paul McCallum had a header from a corner, after good work from Angelo Balanta and George Saunders, deflected behind.
The home side then enjoyed a spell on top around the quarter-hour mark, but Daggers held firm and Matt Robinson produced a strong run which led to another corner.
Saunders also made a good run along the touchline to win another corner, before Dean Rance collected the first yellow card of the day.
And after a good passing move, Robinson saw his shot miss the target on 33 minutes.
Bromley opened the scoring moments later as Cheek smashed past Elliot Justham, before good work from Kenny Clark and Wright led to a chance for McCallum to reply, but he stabbed over the crossbar.
And the visitors went close again in the last minute of the first half as Balanta forced a brilliant save from Cousins.
Balanta was thwarted by Cousins twice more in the second half as Daggers enjoyed a spell of sustained pressure around the hour mark, and McCallum headed inches wide from Wright's superb cross on 69 minutes.
Daggers boss Daryl McMahon made a double change soon after, as Mauro Vilhete and Mo Sagaf replaced Saidou Khan and Liam Gordon and Vilhete had a header cleared off the line just minutes after joining the action.
Cousins made a low save to keep out McCallum, before Vilhete saw a shot deflected behind for a corner on 75 minutes and Adrian Clifton replaced Robinson for the closing stages.
And Cousins was at it again to deny another low shot from McCallum with eight minutes remaining, as Daggers continued to push in search of an equaliser.
Justham had to make a vital save to prevent James Alabi from doubling Bromley's lead on 85 minutes, with Daggers then given four minutes of stoppage time to try and rescue a point.
Bromley were reduced to 10 men when Luke Coulson was shown a straight red card, but the home side held on to claim the points.
Daggers welcome Eastleigh to Victoria Road on Tuesday (April 13, 7pm).
Dagenham & Redbridge: Justham, Johnson, Rance, Clark, McCallum, Balanta, Robinson (Clifton 78), Saunders, Wright, Khan (Vilhete 70), Gordon (Sagaf 70).
Unused subs: Reynolds, Jones.
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