Relegation-haunted Argyle have collected five points in three unbeaten matches since John Sheridan took charge.
Their on-loan Ipswich forward Ronan Murray came closest to breaking the deadlock after 33 minutes when he turned Jason Banton's cross from the left off the face of the crossbar from six yards out.
Banton - signed on transfer deadline day from Crystal Palace - forced Daggers goalkeeper Chris Lewington into a close-range save at the foot of a post seconds before half-time.
The visitors, who started striker Ben Strevens in attack with Sam Williams, had most of the possession but were limited to long range strikes.
Plymouth keeper Jake Cole did well to keep out Luke Howells deflected rising shot after 18 minutes while Billy Bingham fired wide and Strevens and Williams both sent efforts over the bar.
Sheridan's side started the second half brightly with Conor Hourihane testing Lewington with a low angled drive from the left after being put in on goal by Onismor Bhasera.
From the corner, taken by Murray, Femi Ilesanmi cleared Reuben Reid's downward header off the line under pressure from Guy Branston.