The home side opened the scoring in the fourth minute when Colin Daniel played a neat one-two with Emile Sinclair, before threading a pass for Ben Wright to slot home his second goal in three games.
Paul Bolland then capitalised on a slip from Alex skipper Danny O’Donnell to run 30 yards before unleashing a shot under Steve Phillips.
Steve Schumacher then twice went close from the edge of the box for the visitors before former Crewe player Daniel lashed home a stunning 35-yard drive to give Macc a three-goal lead.
Crewe dominated the second half and were given a lifeline in the 64th minute when Macc keeper Jon Brain dropped a John Brayford cross under pressure from sub Calvin Zola, who turned on a loose ball to bag his 14th of the season from 10-yards.
Alexandra then went in search of another goal but the home side sealed the three points in injury time when sub Ricky Sappleton brushed aside the central defenders to bundle home his fifth goal of the season from close-range.