A 77th minute penalty from Michael Rose earned Morecambe a scrappy but deserved point at Rodney Parade.
Rose kept his cool to send Joe Day the wrong way from the spot after the home keeper had brought down Garry Thompson in the box after a fluent Morecambe move.
The Shrimps had to come from behind after Newport took the lead in the 14th minute after conceding a sloppy opener.
Robbie Willmott played a hopeful ball into the Morecambe area and as defenders failed to clear their lines Ben Tozer nipped in and poked the ball past the helpless Barry Roche from six yards out.
Morecambe boss Jim Bentley made three changes to the side at lost narrowly at Luton on Saturday with Alex Kenyon, Adam Campbell and Kevin Ellison coming in for Aaron Wildig, Garry Thompson and Andy Fleming.
After a sluggish start the Shrimps began to find their feet and threaten the home goal after going a goal down.
Steve Old failed to get the killer touch to a bouncing ball in the box as Newport failed to clear a comer before Michael Rose tested Joe Day with a long range shot that the keeper scrambled to safety.
Max Muller also forced Day into a neat save low to his left after driving in a left foot shot from the edge of the area.
Despite the Morecambe pressure it was Newport who came closest to scoring a second in the first half when former Shrimps striker Padraig Amond saw a header from Willmott's corner cleared off the line by Kevin Ellison.
The second half produced few chances until the final stages.
Morecambe looked brighter when Thompson came off the bench and the substitute forced Day into a fine save after running through on goal following a neat one two with Muller.
Thompson's persistence paid off with the penalty but from there the home side were grateful to Roche who saved well with his feet from Amond before a stunning late save to tip away Shawn McCoulsky's close range drive.
The Shrimps almost pinched it at the death when Ellison flashed a shot that was heading for the top corner but was inadvertently blocked by Old and flashed the wrong side of the post.
Newport: Day, O'Brien, Demetriou, Butler, Tozer, Sheehan (rep Osadebe 66), Bennett, Willmott, Amond (rep Hayes 86), Nouble (rep McCoulsky 73). Subs not used: Bittner, White, Reid, Collins.
Morecambe: Roche, Lavelle, Old, Muller, McGowan, Rose, Kenyon, Conlan, Campbell (rep Lang 64), Ellison, McGurk (rep Thompson 64). Subs not used: Nizic, Brough, Fleiming, Wildig, Lund.
Ref: K Johnson.