Shaquile Coulthirst and Ricardo Santos were the two goal scorers as Barnet clinched vital points at the Hive.
The hosts got off to the best start possible after Coulthirst broke the deadlock with only 10 minutes on the clock after turning his man and burying his effort low into the back of the net.
After the crossbar denied Newport from drawing level, Barnet could have been two up when Richard Brindley saw his effort blocked off the line.
The full-back was in the thick of it again when his free-kick forced Joe Day to make a low save to his right after David Tutonda was brought down with 25 minutes on the clock.
The Bees continued to show sheer desire when Brindley posed a threat yet again after coming back onto the field following treatment to his head. He burst down the right flank before crossing into Simeon Akinola but his close range effort failed to trouble Day.
Martin Allen’s side maintained their search for a two-goal cushion and Brindley could have delivered but his free-kick from outside the area deflected into the hands of the Newport goalkeeper.
Barnet showed no signs of ending their dominance and Coulthirst nearly added to his goal tally but his shot from the edge of the box deflected off an Exiles defender out of danger.
The first half was undoubtedly all Barnet and John Akinde nearly made it two on the stroke of half-time when he beat Day to a one-on-one but his header was cleared off the line by Ben White.
The Bees began the second period exactly how they ended the first; Akinde cut inside from the left wing and fired a shot at goal which was parried out of danger by Day.
Just shy of the hour mark and the visitors started to flex their muscles as Padraig Amond drilled in a dangerous cross into the box but Santos was on hand to clear his lines.
However, it was Barnet who had the next chance to find the net when Akinola played in Akinde from the left but his effort on the turn from close range fell wide of the post following pressure from the Newport defenders.
The Bees then had two chances in the space of a minute to go two up as Santos’ curling effort from the edge of the area was palmed away. Seconds later, Brindley cannoned a volley from the right side of the box which whistled inches wide of the post.
The constant second half pressure and dominance from the Bees soon paid off with nine minutes remaining after a Watson corner was headed home by Santos to double the hosts’ lead.
It could have been three in stoppage time as Jean-Louis Akpa Akpro let fly from distance but his effort could only lead to a corner.
However, that miss didn’t matter as the Bees claimed all three points in what was undoubtedly one of their best performances of the season.
We travel to Morecambe next Saturday as the fight for survival continues.
Bees side: Ross, Brindley, Santos, Nelson, Weston, Akinde, Coulthirst (Akpa Akpro), Tutonda, Akinola (Payne), Nicholls, Sweeney (Watson)
Unused Subs: McKenzie-Lyle, Clough, Bover, Fonguck.
Attendance: 1,816 (240 Newport)