The Pilgrims took a 25th minute lead when Paul Wotton thrashed the ball in from a penalty, awarded for a foul on skipper Conor Hourihane by Town target man Jon Parkin from a Andres Gurrieri corner.
The home side doubled their advantage in the 39th minute when Jason Banton drilled a low shot into the bottom corner from 20 yards.
Argyle keeper Jake Cole then made a brilliant reflex save to keep out Junior Brown's exquisite chest down from Alan Goodall's cross in first half stoppage time.
Fleetwood's David Ball reduced the deficit in the 75th minute when he latched on to a bouncing ball to power a left-foot volley past Cole from an angle.
And Cole went full stretch to flap over substitute Barry Nicholson's 18-yard strike that looked to be heading into the top corner as Fleetwood piled on the pressure.
The Cod Army were then reduced to 10 men in the 85th minute when Paul McKenna received a second yellow card.