The Foxes' fifth straight win was tough on the struggling Cumbrians, who pushed the visitors all the way and may have had better luck but for some controversial refereeing decisions.
Leicester boss Nigel Pearson was returning to Brunton Park for the first time since he was in charge of Carlisle when Jimmy Glass scored the last-gasp goal that kept them in the Football League in 1999.
He admitted: "Carlisle caused us problems. They worked hard and pushed us all the way and they played with quality as well.
"They put on a good performance. They'll be disappointed not to get anything out of this but I've no apologies. I thought we were worthy winners in the end.
"I think we created more chances and overall were the better side."
Carlisle boss Greg Abbott was disappointed: "Leicester are a tough and decent side and they know we've pushed them to the wire.
"We made them play to the maximum of their ability. The margins in this game are small and both sides went for the win."
Danny Graham opened the scoring in the 27th minute. After he was fouled just outside the box, Leicester failed to clear Graham Kavanagh's free-kick and Graham forced it past Dave Martin from close range.
Andy King levelled the scores in the 59th minute lashing in a fierce shot from just outside the box.
And ten minutes later Leicester took the lead. The visitors hit Carlisle on the break and Steve Howard's deflected shot hit the bar and went for a corner.
Swiss international Bruno Berner was on hand to force home the dead ball from inside a crowded penalty box.