They got off to a flying start, with new boy Glenn Murray firing home after just four minutes.
In the starting line-up for the first time, Murray snapped up the loose ball from a couple of yards when Morecambe keeper Adam Sollitt could only parry a fierce 25-yard free-kick from Andy Preece.
And Preece made it two when he climbed to glance home a Peter Murphy free-kick in the ninth minute.
But Morecambe, with a fistful of players ruled out through injury and flu, refused to lie down and pulled a goal back in the 20th minute.
Garry Hunter ran on to a defence-splitting ball from impressive Michael Twiss and when Carlisle keeper Matt Glennon beat out his shot, he stabbed the rebound back across the six-yard box for burly Wayne Curtis to apply the finishing touch.
Glennon kept out a Twiss shot after a solo run with an outstretched leg and Twiss should have supplied unmarked Lee Elam in the 29th minute, but shot for goal and Glennon denied him.
Six minutes before the break Morecambe gifted Carlisle another goal - Sollitt and defender Michael Howard leaving a Preece cross to each other for Magno Vieira to gratefully snap up the chance from six yards.
But Carlisle couldn't hang on to their lead and after a 62nd minute run and cross by Dave Perkins, Hunter scored at the second attempt after Glennon had blocked his first, point-blank shot.
With both defences looking jittery, a goal could have come at either end but it was Morecambe who made sure of a point when Curtis curled over a 77th minute cross and substitute Gary Thompson rose unchallenged to plant home a far-post header.