Goals from Steven Howard and Matt Fryatt had given the Foxes a comfortable cushion, but then there were anxious moments late on after a Chris Shuker strike sparked a Rovers rally.
But City's nerves were soothed deep in time added on when Fryatt struck again to make the game safe.
Rovers had toiled hard in midfield from the start to peg back the home side.
But the Foxes had their noses in front on 33 minutes when Lloyd Dyer slipped a quick free-kick to the unmarked Matty Oakley whose cross from the right was bundled home by Howard.
The ex-Derby hit-man was denied a second, a minute before the break, when Tranmere keeper Danny Coyne got a hand to the striker's goal-bound shot.
City found themselves two up on 52 minutes with another goal from a set-piece, this time Max-Alain Gradel whipping in a free-kick from the left for Fryatt to take full advantage of a static defence to thump home a header from close range.
Tranmere hit back with a fiercely struck free-kick from substitute Shuker, but David Martin had positioned himself well to make a comfortable save.
Then the on-loan Liverpool keeper was alert to punch clear an Antony Kay shot, but there was little Martin could do on 80 minutes to prevent an unmarked Shuker sweeping home from close range a Bas Savage cross from the right.
City were denied a late penalty when Ian Goodison appeared to bundle over Fryatt inside the box.
But then deep in stoppage time Fryatt made the game safe, when he nodded home after Coyne had scooped away Howard's initial header.