Chris Hughton’s side have been sucked into relegation danger in the Premier League after six games without a win.
But the Seagulls made the most of a welcome break from the grind of the relegation battle as they saw off Frank Lampard’s Championship side at the Amex Stadium.
Derby had claimed the scalps of Manchester United and Southampton in domestic cup competitions this season.
But the fifth round tie was tipped in Brighton’s favour by a dominant first-half display.
Brighton opened the scoring after 33 minutes when Knockaert bent his first-time shot into the bottom corner of Kelle Roos’ net after connecting with Yves Bissouma’s cross.
Hughton’s team doubled their advantage when Locadia fired home from close-range in first-half stoppage time after Bissouma’s effort hit the post.
Former Chelsea and Arsenal star Ashley Cole set up a tense finish when the Derby defender headed in after 81 minutes.
It was the 38-year-old’s first goal in England since 2012 and his first ever in the FA Cup and the landmark strike came in his second game since joining Derby until the end of the season following his release by LA Galaxy.
But, despite Derby’s barrage of pressure, Cole’s goal wasn’t enough to spark a late escape for the Rams.