Argyle's new left-back Anthony Charles immediately endeared himself to home fans with a first half goalline clearance from Stanley danger man James Beattie.
Beattie was first to Charlie Barnett's corner from the left and his powerful glancing header arrowed towards the far post, where Charles was able to head clear.
Accrington keeper Cameron Belford then made a superb stop to keep the game goalless in the 53rd minute when he managed to block Onismor Bhasera's close-range shot, pushing the ball around a post from point-blank range.
Plymouth's on-loan Yeovil striker Reuben Reid, back for his second spell with the Pilgrims, then fired over when well-placed in the 64th minute.
Belford made a brilliant save with his trailing leg to turn over Reid's 77th minute goal-bound strike from the edge of the six yard box following Charles' deep far post cross.
And then Bhasera and Reid were unlucky not to connect with a free kick from substitute Luke Young that flew across the face of goal as Plymouth pressed.