Stafford boss Phil Robinson made two changes to his side with winger Danny Edwards given a first start of the season, while Ritchie Sutton returned at right-back after a lengthy injury lay-off.
Dagenham boss John Still welcomed Shane Blackett back into his defence in place of Tim Cole.
Early exchanges were confined to midfield before a mistake by Robin Gibson almost let in the Daggers. Sam Sloma picked up a loose pass and threaded the ball towards Paul Benson who couldn't get on the end of it.
The visitors continued to impress and Danny Alcock punched a dangerous cross from Scott Griffiths clear before Wayne Daniel cut out Danny Foster's low centre at the expense of a corner.
Stafford were forced to withstand plenty of pressure on their first appearance in from of the live Sky cameras, but they did have the first attempt on goal in the 16th minute.
Kevin Street crossed from the right towards the far post where Gibson got in a header, but Tony Roberts was well-positioned to save with Neil Grayson lurking to take advantage of any slip-up.
However, Dagenham & Redbridge turned their bright start into a goal when they scored in the 22nd minute.
Glen Southam drilled a penalty into the bottom left-hand corner after Craig-Mackail-Smith had been brought down by Nathan Talbott.
The home side, looking to end a run of three straight defeats, quickly responded with Ged Murphy firing across the face of goal.
Benson drove straight at Alcock as Daggers went close again.
On the half-hour, Stafford felt they were denied what they thought was a penalty when Gibson went down inside the area, but the referee ruled in favour of the Daggers defence.
Rangers certainly became fired up by the referee's decision and impressed during the closing stages of the first half with Gibson and Street in particular causing problems and they were rewarded with an equaliser scored in first-half stoppage time.
Roberts punched Edwards' cross to Gibson who chipped the ball towards goal and Grayson fired into the roof of the net in the scramble that ensued.
Stafford continued where they left off after the break and almost took the lead early in the second half. Street fired a shot across the face of goal from the right which the diving Roberts acrobatically pushed away.
Roberts then pulled off another good save to keep out a close-range effort from Street.
But Dagenham & Redbridge aren't second for nothing and they stunned Stafford with a breakaway goal in the 59th minute which proved to be the winner.
Substitute Cliff Akurang, who replaced Sloma, raced down the right and crossed low for Benson to slot home from close range.
Rangers went on the attack and Street pulled the ball back into a populated area but Grayson shot wide.
Having to do plenty of defending, the Daggers could only attack in patches and Mackail-Smith sent a dipping shot wide in the 71st minute.
Daggers keeper Roberts remained alert and pulled off a good save to hold a deflected 25-yard shot from Grayson.
In the end, Stafford couldn't get the equaliser they deserved with Guy Madjo sending a late shot wide.