John Sheridan remains unbeaten as Argyle manager, but would have been disappointed not to beat relegation rivals Accrington Stanley.
The visitors had the best chance of the first half. Former Southampton and England striker James Beattie saw his header cleared off the line by Onismor Bhasera.
Bhasera almost gave the Pilgrims the lead early in the second half, but his shot was tipped around the post by Cameron Belford.
New Plymouth signing Anthony Charles had the ball in the net midway through the second-half, but his header, from a Ronan Murray free-kick, was disallowed.
Another new player, Reuben Reid, also went close to breaking the deadlock, but in the end Argyle had to settle for a point.
With bottom club Bristol Rovers winning at Rotherham, it's getting very tight at the foot of the table.