Sam Foley hit a hat-trick as Newport fought back to earn new boss Justin Edinburgh his first win in charge.
Gareth Seddon tapped the home side in front inside a minute, only for Foley to level with a copycat strike.
Danny Rose put Newport ahead from the spot after Rob Atkinson fouled Craig McAllister before Foley scored his second on the half hour.
Foley completed his treble from the edge of the box before Seddon was sent off for a second yellow card.
Edinburgh's first win since succeeding Anthony Hudson as boss, against high-flying Fleetwood, was also Newport's first in 13 games - and only their second Blue Square Bet Premier victory of the season.
VIEW FROM THE DRESSING ROOM
Newport County manager Justin Edinburgh told BBC Radio Wales:
"After a disastrous start again the boys showed a great deal of character against a very good side.
"Credit to them - they've come back and got the victory.
"I thought it was a very good performance tonight and obviously delighted for the travelling supporters that have turned out up in great numbers."