The winning goal came in the 67th minute after Torquay right-back Dale Tonge fouled Medy Elito and the Dagenham forward got to his feet to plant his penalty past Martin Rice.
The defeat leaves Torquay eight points adrift of safety with three games remaining, with a Devon derby trip to Exeter on Monday in the offing.
It took the goal to up the ante and Torquay poured forward, with Elliot Benyon smashing a 76th-minute angled drive from the right just over.
At the other end Luke Howell fired just wide as Billy Bingham's corner fell to him at the far post.
The closest Torquay came to levelling was through central defender Krystian Pearce, their outstanding player.
Pearce had an 82nd-minute shot cleared off the line by Dagenham defender Femi Ilesanmi following substitute Jordan Chapell's corner from the right.
Pearce had been denied earlier in the sixth minute from Courtney Cameron's free-kick, with Chris Lewington denying him twice from close range.