Millwall should have had the game dead and buried in the first half but poor finishing from Lewis Grabban and Gary Alexander let the Cumbrians off the hook.
However the visitors were finally undone following striker Kandol's 62nd-minute arrival with the Leeds loanee cleverly flicking over Carlisle keeper Tim Krul in the 90th minute.
The Lions had the perfect opportunity to take the lead in the 31st minute only for Grabban to be denied by the feet of on-loan keeper Krul.
Carlisle pressed and nearly stole a goal before half-time but former Middlesbrough striker Danny Graham failed to trouble Lions keeper David Forde.
The Lions defence never looked like conceding in the second half and Kandol added the killer touch in the 90th minute to keep Millwall's promotion hopes alive.