The Seagulls opened the scoring at the Amex Stadium in the 18th minute through Manchester United loanee Jesse Lingard before Chris Martin levelled from the penalty spot for the Rams just over 10 minutes later.
Brighton were then undone by an unlucky own-goal which saw Martin's shot deflect off the crossbar and in off the back of goalkeeper Tomasz Kuszczak on the stroke of half-time which was a crushing blow to the home side.
After the match, Seagulls boss Oscar Garcia felt his side were dealt with harshly by both the result and the referee after seeing a couple of penalty shouts turned down by Roger East.
"It was a totally unfair result," said the Spaniard. "We were better than them in all areas apart from the most important area, in front of goal.
"If the referee had given us the penalty, it would have been an even better start for us, and then another in the second half. But the referee didn't give them and that's it.
"It's difficult to play the third best team in the league and the top scorers in the league. They are a very good side, so I'm really happy with the performance."
Brighton will now head to the iPro Stadium on Sunday for the return leg with Derby which comes after the first leg of the other play-off semi-final between Wigan Athletic and QPR on Friday night.
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