Ian Craney was the visitors' hero with a goal on 14 minutes which gave John Coleman's improving side an excellent three points.
They were made to fight all the way by League Two new boys Morecambe who dominated the game in the second half but could not find their way through a very resolute Stanley defence which saw Pater Cavanagh and Mark Roberts in outstanding form.
The only goal of the game may not have been pretty but it was certainly important.
Craney, back at his former club on loan from Swansea, hit a wicked inswinging free kick which beat flat-footed Morecambe keeper Steven Drench who was left stranded as defender Ryan Cresswell failed to clear the danger.
Stanley started the game the brighter and before the goal came close when central defender Roberts hit the crossbar with a volley from 10 yards out.
They maintained the pressure after the goal with nippy striker Roscoe D'Sane causing Morecambe's defence all sorts of problems.
He saw one goalbound effort cleared by Shrimps' skipper Jim Bentley before Roberts was denied again by a neat save from Drench.
As the game wore on Morecambe began to take control and bombarded the Stanley goal.
After a quiet opening Carl Baker began to become a greater influence on the game and he was denied a penalty when clipped by Graham Branch in the box as the first half came to a close.
The Shrimps were also denied an equaliser by a string of fine saves from their former keeper Iain Dunbavin.
The Stanley stopper saved sharply from Matty Blinkhorn and Wayne Curtis in the first half and then produced the save of the game to tip away Baker's superb curling free kick in the second period.
Morecambe skipper Bentley volleyed wide from a golden opportunity but was denied a late goal by a superb goal line clearance from Jay Harris as Stanley fought bravely to defend their advantage and clinch their third win in four games.