Looking for only their second win of the campaign, Scunthorpe raced into a second minute lead from their first corner of the game.
It was only half cleared to Terry Hawkridge who returned it into the middle for lively striker Sam Winnall to head home for his second goal in successive games.
Deon Burton had a chance to increase the lead before Newport began to grow into the game.
Midfield man Robbie Willmott drove the Welsh side forward but he might have done better with one good run into the box when he could not get enough power behind his shot to beat goalkeeper Sam Slocombe.
Newport threatened most with their aerial power without being able to get anything else on target in an evenly balanced first half.
But three minutes into the second half the visitors were so very nearly back on level terms when a header from Lee Minshull forced a finger-tip save from Slocombe at full stretch to his right following a right-wing cross from David Pipe.
Newport did deservedly level in the 62nd minute when a corner was headed down in a crowded box for defender Andrew Hughes to lash home a shot from 10 yards.
Hughes might then have won it for Newport when he headed over from another corner that the Scunthorpe defence could not deal with.