A first-half header from Colin Coates gave the Crues their first win at Windsor Park in 13 years.
Linfield made the early running and Mark McAllister and Philip Lowry went close before the visitors scored the only goal seven minutes from the break.
Martin Donnelly's pinpoint corner was powerfully headed in by Northern Ireland defender Coates.
Both side created second-half chances and Crusaders keeper Chris Keenan made a fine save to deny Michael Carvill.
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