City took their unbeaten run to 18 league and cup matches but battling Argyle took more from this result.
An organised defence blunted City's free-scoring attack and Scott Murray had a quiet game on their right and did not have a chance to add to his 17 goals.
Plymouth had done their homework and stretched their own run to seven games without defeat and they could have done better as they had their chances in the second half to take all three points.
Argyle were left rueing missed chances when Dave Norris and Marino Keith had shots charged down.
A mistake by home defender Danny Coles also saw Keith break through to hit a post in the same spot City's Lee Peacock had found in the first half.
City might have found themselves behind in the second minute when Paul Wotton's 30 yard free-kick sailed through a poor defensive wall, but Steve Philips was alert and turned the shot away for a corner.
Argyle had a clutch of shots all of which were off target, but it was another setpiece which carried the most promise.
Tony Barras took a free-kick behind the home defence but it was just out of Steve Adams's reach as he slid in.
Barras went off before half-time with a leg injury and Plymouth lost a little of their midfield edge as Wotton dropped back.
City were struggling to make full use of their crosses and, although no-one matched the speed of Christian Roberts, his partnership with Peacock failed to gel where it mattered.
Roberts made way for teenager Liam Rosenior early in the second half shortly after picking up a harsh booking.
Rosenior's exciting young skills promised to unlock the stalemate but a sell out crowd of 18,085 went home without a goal to celebrate.