Nicky Forster collected a long ball before slotting home close to the final whistle to seal victory for Brighton.
Adam Virgo missed from 12 yards for Brighton but did open the scoring when his looping header from Kevin McLeod's cross beat Steve Collis.
Collis denied Steve Thomson while Colin Hawkins hit the Crewe woodwork and James Bailey cleared off the line.
But having weathered the storm, Crewe levelled after Ben Rix picked out Calvin Zola before Forster struck.
Crewe: Collis, Woodards, McCready, Baudet, Jones, Bopp (Rix 16), O'Connor, Bailey, Grant (Moore 86), Miller (Elding 66), Zola. Subs Not Used: Pope, Abbey.
Booked: O'Connor.
Goals: Zola 85.
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Brighton: Kuipers, Whing, Elphick, Hawkins, Richards, Cox, Virgo, Thomson, McLeod, Murray, Forster. Subs Not Used: El-Abd, Livermore, Hart, Robinson, Fraser.
Booked: Forster.
Goals: Virgo 36, Forster 90.
Att: 4,557.
Ref: Jon Moss (W Yorkshire).
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