Arber put them in front with a first-half header, but he also pulled off a last-ditch tackle to prevent Bradford City levelling 17 minutes from time.
In-form Dagenham bossed the contest from the start with midfielder Peter Gain pulling the strings and strikers Jon Nurse and Ben Strevens causing problems for City's back four.
The visitors' 3-5-2 formation snuffed the home dangermen out wide in the first period and it was only a matter of time before the Daggers made the most of their aerial dominance at set pieces.
Centre-half Arber failed to connect with a chance after just 15 minutes and City survived other scares before the defender headed them in front just before the half-hour mark.
The home fans were not impressed when the referee's assistant ruled that midfielder Kyle Nix had handled Shane Huke's attempted cross and Arber rubbed salt in the wound by finding space at the back post to head Gain's free-kick past keeper Scott Loach from six yards.
Soon after City again failed to do their job at the back and Arber fired over a cross which unmarked centre-half Ross Smith headed wide.
Daggers keeper Tony Roberts was rarely tested in the first half and City's best chance of scoring came deep into injury-time when midfielder Lee Bullock headed Joe Colbeck's cross wide.
Two minutes after the break City had another let-off when midfielder Glen Southam surged into the Bradford box, but his ten-yard shot clipped the outside of a post with Loach exposed.
City's top-scorer Peter Thorne headed wide on the hour and referee Anthony Taylor waved away two penalty shouts from the home side as Bradford pressed for the equaliser.
Dagenham looked favourites to grab a second with hot-shot Strevens looking a real threat, but referee Taylor handed Bradford a lifeline when he harshly judged that Smith had bundled over Willy Topp in the box.
Substitute Barry Conlon, who had hardly had a touch, stepped up to take the disputed penalty, but his low left-foot strike was brilliantly parried by veteran keeper Tony Roberts.
The rebound, however, looked to be rolling kindly into the path of Alex Rhodes, but as he threatened to pull the trigger from ten yards, Arber appeared from nowhere to block his effort and clear the danger.
His courageous effort was rewarded 11 minutes from time when Strevens wrapped up the win with a clinical finish.
Hard-working winger Scott Griffiths showed his pace to surge down the Bradford right and, when he drilled a low cross into the six-yard box, Strevens timed his run perfectly to guide the ball past the stranded Loach from close range.