The Foxes conceded a goal deep in injury time which saw their lead over second-placed Peterborough United reduced to two points.
The Foxes were defied by a series of fine saves by Carlisle keeper Ben Williams.
The visitors then stunned the Walkers Stadium by taking a shock lead. Graham Kavanagh played a through ball which split the City defence and allowed veteran Michael Bridges to run on and curl a 16-yard shot beyond the advancing Tony Warner.
Leicester then fought hard for an equaliser but couldn't find a way past Williams, who tipped over Matt Oakley's 25-yard piledriver and then somehow clawed away Matty Fryatt's close-range flick.
The Carlisle keeper was finally beaten on 52 minutes when Lloyd Dyer's low cross found Matt Oakley, who fired home a fierce shot from ten yards.
Losing the lead, however, did nothing to dampen the enthusiasm of Carlisle, who went close when Bridges shot narrowly wide and Cleveland Taylor drove just over.
But, thereafter, City dominated but struggled to break down the resolute Cumbrians.
Andy King threatened on 85 minutes, but his 25-yard drive was tipped away by Williams.
Leicester finally got themselves in front with two minutes remaining when, from a quick break involving Liverpool loanee Astrit Ajdarevic and King, Dyer crossed for Matty Fryatt to head home what appeared to be City's winner.
But the home side switched off in time added on to allow Scott Dobie to convert Michael Liddle's cross with an unmarked header.