Aaron Downes' header just after half-time handed Alan Knill's Gulls only their fifth victory of the season and came after last weekend's 1-0 win over Southend.
Dagenham were on top for most of a goalless first half, although Torquay missed arguably the best chance.
Zavon Hines saw an early shot superbly saved by goalkeeper Michael Poke, while Femi Ilesanmi also went close to opening the scoring for the hosts.
Again Torquay 'keeper Poke made an alert stop to keep out Medy Elito, before the visitors fluffed a great opening just before the interval when John Marquis fired disappointingly straight at Chris Lewington.
But the visitors made no mistake five minutes into the second half when Downes opened the scoring as he convincingly headed home Jak McCourt's cross.
Dagenham were then denied by the woodwork as striker Rhys Murphy saw his drilled effort bounce out off a post.
Marquis almost made it 2-0 to the visitors in the 89th minute but Lewington again denied him with a smart stop.