First-half goals by Anthony Knockaert and Jurgen Locadia proved to be enough to secure victory for Chris Hughton’s side, who were knocked out of the competition by Manchester United last season.
In a lively opening to the fifth-round tie, Knockaert had an early free-kick saved by Rams goalkeeper Kelle Roos while Yves Bissouma blasted a shot high and wide.
The Seagulls deservedly took the lead in the 33rd minute when the impressive Knockaert fired a low shot past Roos after Bissouma had set up the Frenchman.
The Championship side struggled to create many clear-cut openings throughout the 90 minutes and it came as little surprise when the Seagulls doubled their lead in first-half stoppage time.
Bissouma’s shot beat Roos but hit the post and Locadia was on hand to turn the rebound home.
Derby boss Frank Lampard opted to bring on Ashley Cole for the second half but the visitors continued to struggle after the interval.
Jack Marriott had a shot blocked but Brighton went close to extending their advantage when Roos tipped Knockaert’s fierce drive over the bar.
The visitors appeared to be heading out of the competition with a whimper but they halved the deficit with nine minutes left when the 38-year-old Cole nodded the ball into an empty net after Brighton had failed to clear the initial danger.
The goal lifted Lampard’s side but, although they won several late corners, they were unable to take the match into extra time.
Derby will now focus their attention on cementing a place in the Championship play-offs while Hughton will be keen to lift Brighton away from relegation danger - the Seagulls’ next game is at Leicester City on February 26.