The Rams were trailing to Jesse Lingard's 18th-minute strike on Thursday night, but Derby's top scorer Chris Martin levelled from the penalty spot before the half-hour mark for his 24th goal of the season.
The striker then saw his long-range effort in first-half stoppage time come back off the crossbar and bounce in off the back of luckless Seagulls keeper Kuszczak to ensure Derby take a slender lead back to the iPro Stadium for Sunday evening's return leg.
County, rejuvenated under former England boss Steve McClaren, were favourites going into the tie having finished 13 points ahead of their opponents and beaten them twice already this season, while they booked their play-off spot more than three weeks ago.
Brighton, by contrast, left it to the final minute of the final day to snatch sixth place from Reading, yet it was the hosts who drew first blood.
In the 18th minute, Andrea Orlandi and Will Buckley combined to send Inigo Calderon charging to the byline and the Spaniard's cut-back was turned in at the second attempt by Manchester United loanee Lingard.
But Derby drew level just before the half-hour when Craig Forsyth jinked into the area only to be halted by a clattering foul by Matt Upson.
It was an uncharacteristic and costly error from the former England international, Brighton's player of the year, as Martin stepped up to convert from the spot.
It only added to the frustration felt on the Brighton touchline, with Calderon and Leo Ulloa having been on the end of some dubious challenges in Derby's box but with no consequences for the visitors.
The play-off semi-finals can often be cagey affairs, particularly in the opening stages, but this one was nothing of the sort.
Brighton immediately went in search of the lead again and Ulloa's downward header was well saved by Grant.
But Derby looked the more dangerous side and Kuszczak had to palm away Johnny Russell's cross with Martin poised to apply the finish, before Craig Bryson fired a dipping shot over the crossbar.
And they went ahead in first-half stoppage time when Russell, with his back to goal, played the ball to the feet of Martin who crashed his shot against the woodwork and in off the prone Kuszczak.
Brighton came agonisingly close to an equaliser after the break, but Ulloa's volley was superbly tipped onto the same crossbar by Grant.
Grant was in inspired form after the break and also did well to keep out efforts from Lingard and half-time substitute Kazenga LuaLua as the Seagulls did their best to get back into the match.
But man-of-the-match Grant would not be beaten again as the Rams moved to within a clean sheet of reaching Wembley and the Championship play-off final.