David Ball handed Fleetwood the lead after just 90 seconds, getting the final touch following an audacious overhead effort from Barry Nicholson.
For all their possession Plymouth failed to carve out clear chances and, after Darren Purse's dismissal 12 minutes from time, it was two when Curtis Nelson turned Curtis Obeng's cross into his own net. Junior Brown popped up at the back post deep into injury time to round off the scoring.
Mellon said: "At times we were a little bit rigid. The early goal was exactly what we wanted but we didn't really take advantage.
"Once we started to play with a little more freedom I think we came into the game and created some good chances.
"To get the three points and to be where we are in the table, you've got to be pleased."