First-half goals from Sol Davis and Paul McVeigh either side of Magnus Okuonghae's equaliser were enough to give the Hatters a vital victory, moving them to minus 11 points at the bottom of the table.
For out of sorts Dagenham it left them with just one win in their last eight outings.
The Daggers started the better and came close to an opener in the third minute when left-back Scott Griffiths hit a 20-yard volley that home goalkeeper Conrad Logan managed to palm aside.
Luton soon settled though and took the lead just three minutes later when their own left-back Davis marauded upfield and, after playing a one-two with Chris Martin, drilled a low left-footed drive into the far corner of the goal from 14 yards.
The hosts kept up the pressure and Kevin Gallen, in on loan from MK Dons, shot wide from 12 yards in the 13th minute, before Michael Spillane saw an angled ten-yard effort blocked by Roberts two minutes later.
Dagenham then rallied and drew level in the 33rd minute when Luton failed to deal with Sam Saunders' driven near-post corner, allowing Okuonghae to prod home from two yards.
The encounter developed into an end-to-end affair with chances at both ends, most notably to Gallen in the 35th minute when Martin seized on Tony Roberts' poor goal-kick and teed up his strike partner, only for Roberts to redeem himself with a point-blank save.
McVeigh then spurned another opportunity in the 38th minute, but made amends in fine style three minutes later when he superbly volleyed home from 15 yards after Mark Arber's woeful clearance allowed Martin to cross from the left.
Luton began the second period just as they ended the first and almost grabbed a third when McVeigh fired into the sidenetting following Jake Howells' 56th minute cross.
If the first half had been free-flowing and entertaining, the second period was exactly the opposite as both sides struggled to create openings in a scrappy affair.
The best chance didn't arrive until the 89th minute when substitute Rossi Jarvis slipped in Gallen, only for Roberts to once again produce a smart save.