A first-half strike from Exiles midfielder Ben Tozer and a second-half penalty from Morecambe captain Danny Rose ensured the points were shared.
Newport opened the scoring when Tozer tapped home after collecting a through ball from Frank Nouble.
But the visitors were a threat on the counter-attack, with Scot Bennett shown a yellow card for a cynical pull-back on Adam Campbell.
Padraig Amond came close to extending the home side’s lead on the stroke of half-time but his close-range header was cleared off the line.
The Shrimpers applied far more pressure in the second half and were awarded a penalty when Garry Thompson was brought down in the penalty box.
Brighton have been linked with a swoop on League One Sunderland for the signature of goalkeeper Jason Steele.
Southampton remain in the hunt for Red Bull Salzburg's Amadou Haidara and are reportedly readying a £15million offer.
Aston Villa are reportedly weighing up a summer move for out-of-favour Huddersfield defender Michael Hefele.
Southampton are lining up a summer bid for Huddersfield Town midfielder Aaron Mooy, reports claim.