Captain Lee Carsley scored the only goal of the game midway through the second half, but the Blues were somewhat fortunate to still be on level terms with the home side by then - and equally fortunate to stay ahead afterwards.
The Pilgrims were made to regret not making the most of some good chances to score throughout the game.
Argyle had lost their previous two games but came out of the blocks quickly and soon had Blues on the back foot.
Paul Gallagher had a shot saved by Blues goalkeeper Maik Taylor, before Jamie Mackie was denied at the last by a sliding tackle from Martin Taylor.
Pilgrims captain Marcel Seip tried a snap-shot from the edge of the penalty box only to find Taylor perfectly positioned.
Gallagher attempted an ambitious bicycle-kick that flew narrowly over the goal before Rory Fallon's header was saved by the overworked Taylor.
Recalled centre-back Krisztian TImar then went close at the far post just before half-time but found the side-netting with his header.
Argyle were let off early in the second half when Radhi Jaidi fired over an unprotected goal from three yards, but Mackie should have opened the scoring when, after seeing Taylor save well from his low drive, he subsequently mis-hit a shot wide from Fallon's cross.
Argyle paid for the miss almost immediately. They survived when Quincy Owusu-Abeyie's drive bounced down off the crossbar, but Carsley was on hand from the subsequent corner to drive home the winner.
Still Argyle attacked and Simon Walton's left-foot drive was spilled by Maik Taylor stopped, before Jaidi nearly turned the ball into his own net from substitute Craig Noone's cross.
Gallagher lifted a shot over after good work by Mackie on the right and Blues survived to take the three points.