The visitors, already relegated, frustrated Rovers for over an hour.
But the breakthrough came in the 66th minute with skipper Jason McAteer heading in his fourth league goal of the season after clever work by Paul Hall.
County could easily have grabbed a third minute lead when Adam Le Fondre put a snap shot inches wide. Then Keith Briggs volleyed over.
But gradually Tranmere took control. Hall shaved a post in the 28th minute. Then keeper James Spencer made important blocks from Ryan Taylor and McAteer before Iain Hume headed just wide when set up by Gareth Roberts.
John Hardiker brought a good save from home keeper John Achterberg soon after half-time, but then it was all Tranmere again. Hall and Taylor went close before the breakthrough came.
It seemed an avalanche of home goals might follow but Hume twice missed good chances.
The visitors made three substitutions to try to salvage something from the game but Achterberg was not really tested.