Steve McClaren's side took a 2-1 lead into Sunday's semi-final second leg at the iPro Stadium and Brighton were unable to produce a fightback as they were outclassed by a clinical Derby side.
A stunning finish from Will Hughes, in for the injured Craig Bryson, gave Derby a half-time advantage and they showed no signs of nerves after the break as Brighton were swept aside in front of a sell-out crowd of over 33,000.
Martin, who had already scored three times against Oscar Garcia's side this season, added a second goal and further strikes from on-loan midfielder George Thorne and Jeff Hendrick stunned Brighton.
Kazenga LuaLua pulled a goal back late on, but the damage had already been done and Derby can now look forward to a Wembley final against either QPR or Wigan Athletic on May 24, while Brighton crash out at the semi-final stage for the second successive season.
On a slick surface following heavy rainfall, Derby midfielder Hendrick was possibly fortunate to escape with only a yellow card for a lunge on Rohan Ince early on.
The home side got into their stride and marauding left-back Craig Forsyth surged forward and tried his luck with a left-foot strike, but his shot found the side-netting.
Derby were in front 11 minutes before the break, though, and Forsyth was the architect as his cross was turned in by Hughes' cheeky finish with the inside of his left foot.
McClaren's men then pressed home their advantage in the second half and Martin was on hand to prod home at the back post after Jamie Ward had headed across goal after 56 minutes.
Thorne then got in on the act with a clinical right-foot volley from long range with 14 minutes left, then Hendrick played a lovely one-two with Patrick Bamford before firing home with his right foot to round off a flowing move three minutes from time.
LuaLua pulled one back two minutes later with a well taken right-foot finish, but it was too little, too late for Brighton.
