The Exiles were reduced to 10 men on 36 minutes when goalkeeper Joe Day was dismissed for bringing down Plymouth forward Jordan Slew.
Argyle's Graham Carey converted the penalty and added another from the spot when he was fouled by Darren Jones.
A fabulous 25-yard volley from County's Jon Parkin had levelled matters earlier on, but Slew's late strike sealed it.
Match ends, Newport County 1, Plymouth Argyle 3.
Second Half ends, Newport County 1, Plymouth Argyle 3.
Corner,  Plymouth Argyle. Conceded by Darren Jones.
Rhys Healey (Newport County) is shown the yellow card for a bad foul.
Foul by Rhys Healey (Newport County).
Yann Songo'o (Plymouth Argyle) wins a free kick in the defensive half.
Corner,  Plymouth Argyle. Conceded by Scot Bennett.
Attempt blocked. Jordan Slew (Plymouth Argyle) right footed shot from the centre of the box is blocked.
Attempt saved. Reece Grego-Cox (Newport County) right footed shot from outside the box is saved in the top centre of the goal.
Attempt missed. Ben Tozer (Newport County) header from the centre of the box misses to the right.
Corner,  Newport County. Conceded by Yann Songo'o.
Attempt blocked. Sean Rigg (Newport County) left footed shot from outside the box is blocked.
Substitution, Plymouth Argyle. Ryan Donaldson replaces James Spencer.
James Spencer (Plymouth Argyle) is shown the yellow card for a bad foul.
Jazzi Barnum-Bobb (Newport County) wins a free kick on the right wing.
Foul by James Spencer (Plymouth Argyle).
Sean Rigg (Newport County) wins a free kick in the attacking half.
Foul by Yann Songo'o (Plymouth Argyle).
Attempt missed. Sean Rigg (Newport County) right footed shot from more than 35 yards is too high.
Goal!  Newport County 1, Plymouth Argyle 3. Jordan Slew (Plymouth Argyle) right footed shot from the centre of the box to the bottom left corner. Assisted by Graham Carey.
Substitution, Newport County. Jack Compton replaces Jordan Green.
Corner,  Newport County. Conceded by Yann Songo'o.
Attempt saved. Graham Carey (Plymouth Argyle) right footed shot from outside the box is saved in the centre of the goal.
Substitution, Plymouth Argyle. Connor Smith replaces David Fox.
Rhys Healey (Newport County) wins a free kick on the left wing.
Foul by Gary Miller (Plymouth Argyle).
Rhys Healey (Newport County) wins a free kick on the left wing.
Foul by Jake Jervis (Plymouth Argyle).
Jordan Green (Newport County) wins a free kick on the left wing.
Foul by Jordan Slew (Plymouth Argyle).
Substitution, Plymouth Argyle. Jake Jervis replaces Craig Tanner.
Substitution, Newport County. Rhys Healey replaces Jon Parkin.
(Newport County) wins a free kick in the attacking half.
Dangerous play by David Fox (Plymouth Argyle).
Corner,  Plymouth Argyle. Conceded by Darren Jones.
Attempt blocked. James Spencer (Plymouth Argyle) right footed shot from outside the box is blocked.
Attempt missed. David Fox (Plymouth Argyle) right footed shot from the centre of the box is high and wide to the right.
Goal!  Newport County 1, Plymouth Argyle 2. Graham Carey (Plymouth Argyle) converts the penalty with a left footed shot to the bottom left corner.
Penalty conceded by Darren Jones (Newport County) after a foul in the penalty area.
Penalty Plymouth Argyle. Graham Carey draws a foul in the penalty area.
Newport County's plight at the bottom of League Two worsened as they were beaten by leaders Plymouth.