The home side broke the deadlock after 33 minutes when Steve Howard latched onto a Matt Oakley cross to tap the ball into an empty net from close range.
Nigel Pearson's troops continued to press forward with the impressive Howard once again seeing a left-footed drive tipped around the post by goalkeeper Danny Coyne.
Just after the interval, the hosts doubled their advantage as Matt Fryatt latched onto a Max-Alain Gradel free-kick just outside the area and guided a superb header beyond the outreaching arms of Coyne.
A double substitution on the hour mark gave some hope to Ronnie Moore's men and when Chris Greenacre found himself in space down the right he steered an inch-perfect cross for Chris Shuker to hit a right-foot shot home on 80 minutes.
But Tranmere's late pressure was undone when, with the last action of the game, Fryatt again rose well to head home from six yards.