Teenage striker Nicky Maynard was the star of the show with two goals in the second half after Brighton had defender Kerry Mayo sent off in first-half stoppage time.
The home side took the lead against the run of play in the 39th minute with a first senior goal for Dean Cox.
The tiny left winger swept home a shot from outside the area after being set up by Richard Carpenter, with Crewe defenders looking around in vain for an offside flag.
The visitors deservedly pulled level in the final minute of the first half. Brighton keeper Wayne Henderson could not hold a well-struck 30-yard free-kick by French centre-half Julien Baudet and Billy Jones knocked in the rebound.
Worse followed for Brighton in first-half stoppage time when Mayo brought down Maynard inside the box. He was adjudged to be the last defender by referee Jarnail Singh and received a straight red card.
Ryan Lowe sent Henderson the wrong way from the spot-kick to give Crewe the lead their first-half display warranted.
Brighton's hopes of recovering from a man and a goal down were dashed in a matter of seconds in the 55th minute.
They almost equalised when Alex Revell cut inside for a shot which goalkeeper Ben Williams parried and Jones then inadvertently hit the ball against his own post.
Crewe broke immediately and Maynard charged down Henderson's attempted clearance from outside his area before running on to nod the ball into an empty net.
Henderson's mixed afternoon continued as he made superb one-handed saves to deny Maynard and his strike partner Luke Varney twice.
But the Republic of Ireland international keeper was helpless with five minutes left when David Vaughan crossed for Maynard to volley in from close range to round off an impressive Crewe comeback.