The closest Argyle came to breaking the deadlock was in the fifth minute when winger Rommy Boco's angled drive from the right edge of the box clipped off the outside of the far post with outstretched Stanley keeper Marcus Bettinelli beaten.
Bettinelli denied Marvin Morgan in the second minute as the Argyle target man broke through one-on-one.
Striker Reuben Reid fired a 25th minute shot just wide from 10 yards and then missed a golden opportunity to score from Hamza Bencherif's 38th minute nod down, enabling Bettinelli to make a routine save.
It was nearly all Plymouth pressure although visitors Shay McCartan and Kayode Odejayi did send shots just wide as Stanley grew in confidence.
The second half started much the same as the first but Argyle failed to make the most of their territorial advantage, prompting Plymouth boss John Sheridan to introduce home grown playmaker Luke Young and teenage striker Tyler Harvey.
Again as the half wore on Stanley grew in confidence, with substitute James Gray looking dangerous.