The Cumbrians came close to breaking the deadlock when Zigor Aranalde floated a free-kick from the left flank towards the back post and Garner headed goalwards from ten yards but goalkeeper Steve Collis saved at the foot of his post.
Southend replied with Alan McCormack picking up the ball just outside the 18-yard box, but his low shot was smartly saved by the diving Keiren Westwood. And the Shrimpers came close to opening the scoring through Steve Hammell, whose left-foot kick cleared the five-man Carlisle wall and forced a fine save from Westwood, who palmed the ball over his crossbar.
The home side went close early in the second half from a Leon Clarke shot following a well-worked free-kick, but on the hour Carlisle took the lead. A centre from Chris Lumsdon in the right channel was knocked down by Danny Graham to unmarked strike partner Garner, who clinically finished from seven yards for his fifth goal of the season.
Westwood then did well to parry a fierce Gary Hooper shot, before Collis did the same at the other end to deny Joe Anyinsah. But Graham was left kicking himself for failing to double the advantage when he stabbed the ball wide of an open goal from three yards. Carlisle hung on for the win though that takes them to the top of the League One summit for the first time the season.