There was not a real chance in the first-half until the 39th minute, when a mistake by City's Michael Morrison let in Bas Savage but David Stockdale turned the shot away for a corner.
Steve Howard twice missed the target for the visitors and Antony Kay and Ben Chorley had no better fortune for the Merseysiders,
Tranmere's opening goal came two minutes after half-time with a fine strike from the corner of the box by Kay when set up by Savage.
The home side continued to hold the upper hand but Terry Gornell saw a 63rd-minute header deflected for a corner and then Savage fired across the face of the goal.
But eight minutes from time Savage was brought down by Chris Powell and Steve Jennings found the right-hand corner with the spot kick.