Crewe recorded their third consecutive Championship victory with a convincing win at Gresty Road.
Skipper Kenny Lunt opened the scoring with a stunning early free kick before Andy White marked his full debut with a thumping effort to put Alex 2-0 up.
Substitute Michael Higdon was on the pitch for only six minutes before he sealed the points with a headed third.
Brighton substitute Albert Jarrett, also making his debut, headed a consolation with 10 minutes left.
Crewe boss Dario Gradi:
"After winning our two previous games you would have thought we'd have played with a bit more confidence.
"We were well off the pace of the game right from the start and our midfield players didn't get tight enough.
"We are probably fortunate we met Brighton and not one of the teams nearer the top. Our attempts to clear the ball near the end of the game were absolutely pathetic."
Brighton boss Mark McGhee:
"We feel a little hard done by and decisions didn't go for us, but that's sometimes what happens.
"But we didn't defend well from their set-pieces and that was a lesson to us.
"I'm not embarrassed by the result, we had a lot of good possession and created chances, so it's onwards and upwards."