The Hatters, marooned at the bottom of the Football League after being docked 30 points, won their third shoot-out of the campaign 4-3 after the game had finished 1-1 after 90 minutes.
The hosts had gone ahead just 60 seconds into the game as striker Tom Craddock capitalised on an unbelievable mix-up in the Brighton defence before slotting home.
But Brighton were level in the 21st minute when Nicky Forster used his pace to latch on to Chris Birchall's through ball before drilling low into the far corner, right-footed from 20 yards for his 13th goal of the season.
On the stroke of half-time the momentum swung back into the Hatters' favour as Dave Livermore was sent off for the Seagulls following his crunching challenge on Michael Spillane.
However, neither side went close to scoring again and it was down to on-loan Derby goalkeeper Lewis Price to perform the heroics as he saved two spot-kicks to spark joyous scenes at Kenilworth Road.