Martin Ling's side had the better of the first half with visiting keeper Jake Cole forced to save from Ian Morris in the 15th minute, and outstanding Argyle left-back Robbie Williams made a crucial block to keep out Lee Mansell's thumping follow-up.
Mansell went close with a dipping 18th-minute half volley before Argyle striker Warren Feeney tested home keeper Michael Poke with a 30-yard drive.
Poke then palmed Williams' free-kick around a post as Argyle finished the half in the ascendancy.
Cole again denied Mansell at the start of the second half as the home skipper powered a header towards goal from the recalled Danny Stevens' left-wing cross.
Poke kept out a Feeney effort on the hour with another diving stop, and minutes later kept out Conor Hourihane's low drive with his feet.