The Bantams last celebrated victory in a 2-0 triumph over Exeter City, a result which was followed by three defeats and two draws in all competitions.
But James Vaughan's 58th-minute penalty proved enough for the three points on Saturday afternoon.
The former Everton and Birmingham City striker won the spotkick when he latched onto a loose back pass before being felled by Newport goalkeeper Nick Townsend.
And he made no mistake from the spot, calmly placing the ball into the bottom corner.
The result puts Bradford up to sixth, two points behind second-placed Exeter and only five behind league leaders Swindon Town.
Aramide Oteh had the host's first opportunity as he worked the space for a shot but was quickly snuffed out by Townsend.
The forward had another chance to grab the opener but blazed an effort over after being slid through by Jake Reeves.
Bradford were hit with a scare early in the second half as Tristan Abrahams struck wide after City were careless with possession.
Just five minutes later though, the Bantams led as Vaughan struck from 12 yards.
Moments later, Oteh's header was pushed onto the post by Townsend as City looked to gain complete control.
The Newport keeper had to be alert again to claim a header from Paudie O'Connor.
Nine minutes of injury time didn't help ease the nerves inside Valley Parade but City saw the game out comfortably to claim all three points.