The visitors deserved at least a point for their gallant second-half fight-back which ended with Craig Stanley missing an equalising chance deep into injury time.
He put his effort over the bar from a cross from Wayne Curtis and with it any hopes of a point vanished.
Wrexham looked well in command after a busy first-half with Chris Llewellyn laying on chances for Michael Proctor to score in the sixth and 22nd minutes.
During this time Morecambe were all at sixes and sevens but were saved from going further behind when Michael Twiss headed off the line to stop Llewellyn scoring a third for the hosts.
Neil Roberts and then Llewellyn also missed chances of completely sealing the game for the home side.
It was Jon Newby, a former Wrexham player, who led Morecambe's fight-back in the second-half when he hit home a Carl Baker cross in the 55th minute to put the skids under the Red Dragons.
Jim Bentley then missed a chance with a flashing header to equalise and Wrexham had to hang on desperately and were mightily relieved when Stanley missed his chance right at the end.