There were 54 places between the two teams at kick-off, in their first meeting since 1985, and the Lions were the better side throughout, despite the visitors' spirited start to the second half.
Millwall, FA Cup quarter-finalists in two of the last three seasons, showed seven changes from their New Year's Day victory over Luton, with only Bartosz Bialkowski, Jake Cooper and Alex Pearce and striker Smith retaining their places.
But they quickly showed that they had the measure of last season's giant-killers and it was Smith who broke the deadlock in the seventh minute.
The former Fulham and QPR target man was afforded far too much time and space at the far post to steer his side in front from a corner and ease any nerves among the home fans.
Mahoney looked like adding a second 10 minutes later after beating two men to wriggle into the box but he lost control as he tried to take the ball around King.
Mahoney was denied again in the 32nd minute when his goal-bound effort was deflected behind by Padraig Amond.
The League Two side, winless in 10 games in the fourth tier, started the second half brightly, with strikers Jamille Matt and Amond both going close to levelling the tie.
Rowett responded by sending on Wales international Bradshaw in place of Smith and the hosts soon had the second goal they craved to quell the Newport resurgence on 64 minutes.
Bodvarsson was fouled in the area by Mark O'Brien and Mahoney sent King the wrong way from the spot to cap his fine display with a goal.
And Bradshaw killed off the contest with a neat lobbed finish at the near post eight minutes from time, with Rowett's men now beaten just once in their last 12 games.