Defender Billy Jones put Crewe on their way to a fifth win in their last six games by blasting in a 23rd-minute penalty after his free-kick was handled by Craig Davies.
Midfielder Steven Schumacher doubled the advantage with a tremendous 25-yard drive in the 79th minute and Jones grabbed his second seven minutes from time with a well-struck free kick from similar range.
Debutant Gylfi Sigurdsson sent Brighton crashing to their seventh defeat in the last nine home league games with a lovely finish two minutes from time.
Brighton, having used their three substitutes, had to play the final 32 minutes with 10 men after defender Jim McNulty was forced off injured.
The Seagulls made a fast start to the second half and Davies forced an important save from Crewe keeper John Ruddy before the visitors ran riot late on.