A goal from Kevin Ellison on his return to the side gave the Shrimps a first win in 10 games.
Ellison scored from close range on 28 minutes after some excellent work from Andy Parrish down the right hand side who produced a cross which was met by the winger who volleyed past Steve Phillips.
The Shrimps were denied a second on the stroke of half time by an offside flag. Phil Jevons's curler beat Phillips but struck the heels of Danny Carlton who was offside and the goal was ruled out.
Crewe have had the majority of the possession and Barry Roche has been forced to make fione saves from Ashley Westwood and Lee Bell.
The second half followed a similar pattern to the first with Crewe having the majority of the possession but Morecambe creating the clearer chances, hitting the woodwork on no fewer than three occasions.
Nick Fenton headed a Lewis Alessandra corner against the post and Alessandra himself struck the woodwork with an excellent left foot drive from an acute angle. Ellison was denied a second by the post when a fierce curler was fumbled by Steve Phillips but the back fell against the post much to his relief.
At the other end Roche made another fine save to de ny Leitch-Smith and the Crewe striker went close with a fine volley from a Byron Moore cross. Former Shrimps' defender Dave Artell also went close with a header from a corner but the Shrimps held on to their advantage with a superb rearguard display.
Boss Jim Bentley made five changes to the Morecambe line up.
Andy Parrish, Phil Jevons, Kevin Ellison, Danny Carlton and Garry Hunter are all included in the starting line up as the Shrimps look to avenge a 2-1 defeat at the Globe earlier this season.
Crewe: Phillips, Davis, Artell, Westwood, Tootle; Lowery, Dugdale, Bell, Moore; Powell. Leitch-Smith. Subs: Martin (GK), Murphy, Mellor, Clayton, Fletcher.
Morecambe: Roche; Parrish, Fenton, McCready, Wilson; McDonald, Hunter, Ellison; Alessandra, Jevons, Carlton. Subs; Routledge (GK), Haining, Drummond, Fleming, Price.
Ref: M Naylor.