Carlisle went into the game without a win at Elland Road, but undefeated away from home since January 29 at Oldham.
Leeds kicked off having lost just one of their last 11 matches.
The game had a 12.15pm kick-off on police advice and Leeds' top scorer Jermaine Beckford passed a fitness test shortly before the start.
Carlisle-born defender Paul Huntington had his head bandaged to protect an injury received at Leyton Orient last week and he and his Leeds colleagues were caught out after only 16 minutes.
Evan Horwood made ground on the left before passing inside to Simon Hackney. His low cross to the far post eluded several players before Scott Dobie ran the ball into the net for his third goal of the season and the first Leeds had conceded in five matches.
Freedman should have equalised four minutes later, but the veteran striker headed Darren Kenton's cross too high from eight yards.
Freedman was also off target with a 12-yard shot shortly before the interval after clever inter-passing by Jonny Howson, Jonathon Douglas and Beckford.
Leeds had plenty of possession, but Carlisle frustrated them in the first half by using a five-man midfield and leaving Danny Graham to forage alone up front.
However, Leeds hit back to lead after the interval with two goals in nine minutes.
Freedman atoned for his earlier misses with a 49th minute equaliser after taking Neil Kilkenny's pass and riding a challenge from keeper Keiren Westwood eight yards out.
Tresor Kandol replaced Beckford and, when the striker's shot was parried, Howson smashed the rebound into the net.
Two minutes later, Carlisle were level when Leeds keeper Casper Ankergren dropped Hackney's corner for Graham to score at point blank range.
The goal spree continued with Leeds regaining the lead on 69 minutes with Freedman's second goal.
Grant Smith fouled Bradley Johnson and Freedman pounced on Kilkenny's free-kick from the left with an unstoppable goalmouth shot that was to prove the game's decisive moment.