City's on-loan Bristol Rovers striker Eliot Richards scored his third goal in two games after being unselfishly teed up by strike partner Tom Nichols to score the 83rd minute winner.
Plymouth top scorer Reuben Reid had taken his goal tally to 20 for the season with the 45th minute penalty opener, coolly slotted past City keeper Artur Krysiak into the corner.
The penalty was awarded when City skipper Danny Coles handled left back Matt Parsons' cross.
Liam Sercombe restored parity in the second half with a 20-yard shot that took a deflection to loop over Argyle keeper Jake Cole in the 69th minute.
Reid had nearly put Plymouth ahead in the 40th minute when he cut in from the left and sent a rising angled strike off the top of the bar.
City started the second half brightly and also hit the woodwork, when young forward Nichols beat Cole with a low shot from the right side of the penalty, which flew back off the post.