Willmott handled on the goal-line to prevent Steven Schumacher grabbing an early lead for the home side, only delaying the inevitable as the former Bury skipper grabbed his first from the penalty spot.
Newport, far from subdued by the early sending-off, took the game to Fleetwood, Scott Davies in the Town goal at full stretch to deny Tom Naylor an equaliser.
Danger man Chris Zebroski twice forced saves from Davies as County looked to beat the odds, Conor Washington then finding a way through and beating the 'keeper but not the woodwork.
However, after the break the home side imposed themselves, Schumacher doubling his tally just three minutes in with a stunning 30-yard shot, curling in off a post.
On-loan full back Charlie Taylor nearly added a third with a dangerous blast from the left channel, Conor McLaughlin also testing Lenny Pidgeley in the County goal.
Fleetwood did add a third, again from the spot, when Taylor was sent tumbling by Ryan Jackson, Schumacher sealing his hat-trick.
Zebroski pulled one back from the spot himself with 20 minutes remaining after Nathan Pond handled inside the box.
But David Ball's low shot from the left made it four for the home side with 13 minutes remaining to seal victory.