The visitors took an early lead when Newport defender Darren Jones turned the ball into his own net.
Stevenage doubled their advantage before half-time as Tom Pett headed in from close range.
Newport stay one point away from safety, while Stevenage climb up to ninth place in the table.
Match ends, Newport County 0, Stevenage 2.
Second Half ends, Newport County 0, Stevenage 2.
Corner,  Stevenage. Conceded by Paul Bignot.
Corner,  Stevenage. Conceded by Paul Bignot.
Substitution, Stevenage. Jobi McAnuff replaces Tom Pett.
Foul by Tom Owen-Evans (Newport County).
Tom Pett (Stevenage) wins a free kick on the left wing.
Attempt missed. Charlie Lee (Stevenage) right footed shot from outside the box is too high.
Foul by Joss Labadie (Newport County).
Rowan Liburd (Stevenage) wins a free kick in the attacking half.
Foul by Marlon Jackson (Newport County).
Jack King (Stevenage) wins a free kick in the defensive half.
Corner,  Stevenage. Conceded by Scot Bennett.
Attempt blocked. Charlie Lee (Stevenage) header from the centre of the box is blocked.
Substitution, Stevenage. Rowan Liburd replaces Harry McKirdy.
Foul by Marlon Jackson (Newport County).
Luke Wilkinson (Stevenage) wins a free kick on the left wing.
Marlon Jackson (Newport County) wins a free kick in the attacking half.
Foul by Steven Schumacher (Stevenage).
Attempt missed. Joss Labadie (Newport County) right footed shot from outside the box is too high.
Attempt blocked. Jennison Myrie-Williams (Newport County) left footed shot from outside the box is blocked.
Luke Wilkinson (Stevenage) is shown the yellow card for a bad foul.
Rhys Healey (Newport County) wins a free kick in the attacking half.
Foul by Luke Wilkinson (Stevenage).
Attempt missed. Harry McKirdy (Stevenage) header from the centre of the box is close, but misses to the left.
Rhys Healey (Newport County) wins a free kick in the defensive half.
Foul by Dean Wells (Stevenage).
Substitution, Newport County. Joss Labadie replaces Ben Tozer.
Foul by Jennison Myrie-Williams (Newport County).
Luke Wilkinson (Stevenage) wins a free kick on the left wing.
Josh Sheehan (Newport County) wins a free kick on the left wing.
Foul by Ben Kennedy (Stevenage).
Foul by Scot Bennett (Newport County).
Ben Kennedy (Stevenage) wins a free kick in the defensive half.
Jazzi Barnum-Bobb (Newport County) wins a free kick on the right wing.
Foul by Tom Pett (Stevenage).
Corner,  Stevenage. Conceded by Ben Tozer.
Corner,  Stevenage. Conceded by Paul Bignot.
Substitution, Stevenage. Charlie Lee replaces Henry Cowans.
Attempt missed. Darren Jones (Newport County) header from the centre of the box misses to the right following a set piece situation.
Stevenage moved to within a point of the League Two play-off places after winning away against Newport County, who remain bottom of the table.