Two goals from Matt Fryatt and one from Steve Howard were enough to maintain Leicester's unbeaten start and put them second in the table.
Max-Alain Gradel hit the bar for City and Craig Curran cleared a shot from Howard, who then put the hosts ahead from Matt Oakley's cross.
Fryatt headed the second from Gradel's free-kick before Chris Shuker replied by heading in Chris Greenacre's cross.
Fryatt made the game safe by heading the third from six yards.
Tranmere Rovers manager Ronnie Moore told BBC Radio Merseyside:
"The quality of the ball in from them was top drawer and if we would have had the same quality we would have probably got ourselves some goals from the set plays.
"I think it's been a good performance from us [but] we have to learn about defending from set plays.
"You look at this result and performance, it's the same result as Swindon but it [the performance] was a million miles apart."
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