United had to do it the hard way again as a first for the club from Angelo Balanta and a tenth of the season for Jabo Ibehre overturned an early deficit to take the Cumbrians to their third consecutive victory in the league.
Carlisle dictated the early pace of the game and a deep free kick from Grainger caused problems as Asamoah pulled off his man. He took it on his chest but the touch was heavy and Passley was able to shield it away.
Dagenham got forward with purpose as they tried to hit on the break but Hemmings was disappointed when he put a dangerous cross across the face of goal. McClure was on his heels and it bounced slowly towards the corner flag.
A fierce long range shot from Balanta was just a whisker away as United asked most of the questions and the hosts should have taken the lead when Ibehre was given acres of space on the right flank. He drew two men and his cut back was perfect for the unmarked Jason Kennedy. He had the width of the goal to aim at but it skipped up awkwardly and he could only place his shot over the bar.
Having held the upper hand Carlisle were given another slap in the face when a deflected delivery from Widdowson hung high in the air as it dropped over Gillespie at the back stick. Christian Doidge made it his own as he jumped high and the keeper had no chance as a firm header sent the ball into the back of the net.
United tried to pick themselves up and Dicker rattled a difficult volley over from 22 yards as he came under pressure. Asamoah was unlucky to be flagged offside when he appeared to beat the trap to go one-on-one with the stopper and Ibehre was stopped in his tracks when he was judged to move too early for a Dicker through ball.
The hosts had to be wary as Dagenham continued to spring forward on the break and Joyce did well to recover and make a tackle to prevent Ferdinand from going clean through.
Dagenham worked hard to close the gaps as United continued to play their passing game and home patience was rewarded when Angelo Balanta controlled the ball on his chest with his back to goal. His first for the club came in spectacular fashion as he spun and volleyed an unstoppable effort past the stranded keeper.
Gillespie had to turn a snapshot from Hemmings over as the Daggers tried to bite back and the big keeper had to take care from the resulting corner as he back tracked to tip the inswinging delivery over the target as it threatened to dip into the net.
Carlisle finished the half on top with some testing deliveries but the 1-1 scoreline was just about right following what had been another intriguing 45 minutes of football.
Corners from Grainger had to be defended as United pushed forward after the break, and a set piece at the other end brought a weak header from McClure which Gillespie pulled into his chest.
United took the lead for the first time on the day when a patient build up pulled Dagenham left and right. An initial cross from Grainger was dealt with but McQueen picked up the second ball and his dipper was perfect for the in-form Jabo Ibehre who guided a lovely header past a helpless spread of the arms from the keeper.
An air shot from Hemmings brought relief as it looked easier to score for the unmarked forward, with the Carlisle defence stretched at the back, and Balanta tried to double his tally for the day when he carried the ball out from the clearance. A gap opened up but he screwed his attempt wide.
Joyce was a yard off when he crunched a 30-yarder through bodies and, as the action swung up and down the pitch, Doidge couldn't quite make it to a whipped far post cross as he threw himself full length to get a touch.
Carlisle thought they'd wrapped it up when Miller moved off his man for a Grainger corner. His header beat O'Brien but Passley had hugged the post and he cleared it off the line just in the nick of time. More set piece deliveries followed and Raynes was unlucky when his header dropped just wide as he also left the keeper standing on the spot.
Osei did the hard work to beat two as Carlisle turned the screw but his shot went high as he cut inside and let one go. O'Brien saved from Kennedy late in the day as the midfielder squeezed a shot through from 14 yards and he did the same again when Osei skipped through, but this time with his legs.
And that was it for real goalmouth action as United watched the clock tick down on their hard-earned win.
United - Balanta (37), Ibehre (53)
Dagenham - Doidge (11)
United - Grainger (86)
Dagenham - Obileye (63)
Carlisle United - Gillespie, Miller, Raynes, Grainger, Dicker, Joyce, McQueen (Thompson 85), Kennedy, Balanta (Hery 75), Asamoah (Osei 71), Ibehre. Subs - Hanford, Brough, Sweeney, Rigg.
Dagenham & Redbridge - O'Brien, Passley, Nosworthy, Boucaud, McClure (Cureton 73), Chambers (Jones 67), Doidge, Hemmings (Hines 67), Ferdinand, Obileye, Widdowson. Subs - Cousins, Connors, Dikamona, Hamalainen.
Referee - Mr Ross Joyce
Attendance - 3,871 (74 away fans)