The Home Park pitch survived a 6.15pm pitch inspection by referee Paul Taylor and City survived first-half pressure from Plymouth before securing victory with goals from substitute Michael McIndoe and Liam Fontaine.
City profited on the hour from some dithering by defender Mathias Doumbe as team-mate Nicky Maynard stole the ball from the Frenchman on the edge of the Argyle penalty area.
He then teed up McIndoe for a shot which crashed in off exposed goalkeeper Romain Larrieu's post.
The visitors completed the win - and their fourth successive unbeaten game - five minutes from time when Doumbe's compatriot Larrieu dropped Lee Johnson's corner at the feet of Fontaine for the centre-back to crash home from unmissable range.
It was cruel luck on Larrieu, who had conceded the corner with a brilliant point-blank save from Cole Skuse that left him winded and may have contributed to his loss of concentration.
Up until Doumbe's mistake, Argyle had not looked in a moment's danger and arguably deserved to be ahead at the interval.
Rory Fallon and Karl Duguid both had shots blocked by desperate late tackles and Jamie Mackie saw his cross-shot beaten out by City goalkeeper Adriano Basso.
However, the nearest they came to taking the lead was when Doumbe's attempted cross from deep took a huge deflection off Marvin Elliott.
Although Basso was horribly out of position and totally wrong-footed, he somehow scrambled back to claw the ball away.
Basso was at it again towards the end of the half, finger-tipping away a shot by Jamie Mackie, while Fontaine - his head bandaged after receiving treatment in the first half - cleared Steve MacLean's header off the line.
Then came half-time and following it, Doumbe's second-half mistake which effectively sealed the Pilgrims' fate.