Crewe remain in sixth place but they extended their winless run to five games with a goalless draw at Accrington.
Both sides came into the game out of sorts but the Railwaymen needed the points more as they look to ensure a play-off place.
There were limited chances in the first half with Crewe testing Radek Vitek twice through Zac Williams and Rio Adebisi, although it was routine for the Manchester United loan keeper.
Stanley did not have a shot on target, Tommy Leigh volleying wide with their best opportunity.
Crewe came out after the break on the attack, firing a number of dangerous crosses and corners into the Stanley area but were unable to find the breakthrough.
Stanley struggled to create clear-cut chances, Josh Woods firing over their best second-half chance, but they last kept a clean sheet nine games ago so that, along with ensuring their League Two safety, was something to celebrate after a turbulent season at the Wham Stadium.
