Argyle goalkeeper Jake Cole made two point-blank saves in the first half from Dwight Gayle to keep the sheet clean at half time after Daggers dominated the opening 45.
In front of London 2012 rowing bronze medallist Greg Searle, who is a big Argyle fan, the Pilgrims never really looked like notching their first goal of the league campaign, with a Matt Lecointe effort late in the first period their only chance of note.
Both Dagenham and Argyle lost their opening games of the season, to Cheltenham and Aldershot respectively, so a point got each of them off the mark. But the home side will feel they did enough to earn all three on offer.
Dagenham continued to press throughout the second half, but were frustrated by the continued excellence of Cole and their own profligacy in front of goal.