The Premier League side showed their class to end the Rams’ Cup run
Ashley Cole turned back the clock as Derby’s FA Cup run came to an end with a 2-1 defeat at Brighton.
The Seagulls advanced to the quarter-finals for the second season running thanks to first-half goals from Anthony Knockaert and Jurgen Locadia.
But they were forced to endure a tense finish when 38-year-old veteran Cole came off the bench and halved the deficit late on.
The FA Cup’s most decorated player, with seven winners medals, nabbed his first goal in the competition and his first on English soil since 2012 with a rare header.
Nonetheless, despite a late onslaught, the Premier League side held on to book their place in the last eight.
Both sides would be forgiven for having one eye on other matters going into this fifth-round tie.
Brighton have been sucked into a relegation battle having not won a Premier League game since the turn of the year, while the Rams are pushing for a Championship play-off place.
Albion left first-team regulars Glenn Murray and Lewis Dunk out of their squad because of slight knocks and Davy Propper was also absent because of illness.
There was a pedestrian pace at the start of the lunchtime kick-off, with neither side really threatening.
Rams goalkeeper Kelle Roos comfortably turned away free-kicks from Knockaert and Bissouma inside the opening 25 minutes.
Referee David Coote then stuck with his initial decision after consulting the video assistant referee having booked Derby winger Harry Wilson for a high challenge on Beram Kayal.
Frenchman Knockaert has not started a top-flight game for two months and appeared keen to seize a rare cup opportunity.
He deservedly put the hosts ahead by clinically sweeping a first-time finish into the bottom-right corner to claim his third goal of the campaign after Bissouma pulled the ball back having exchanged passes with Alireza Jahanbakhsh.
Martyn Waghorn wasted Derby’s first shot on target by scuffing straight at Seagulls goalkeeper David Button in first-half added time, before the home side doubled their advantage moments later.
Bissouma, a £15million summer signing from Lille, worked space on the edge of the box and, after his fine curling effort came back off the inside of the left-hand post, Locadia was alert to tap home.
Rams boss Frank Lampard had plenty to ponder at the break and responded with a double substitution, bringing on 38-year-old former team-mate Cole and Jack Marriott.
The visitors almost produced an immediate response when a powerful, goal-bound drive from Liverpool loanee Wilson was bravely blocked by the head of Shane Duffy.
Derby, who have not reached the last eight of the competition since they were managed by Jim Smith 20 years ago, twice came from two goals down to knock out Premier League Southampton after a third-round replay.
After Roos produced fine stops from both Knockaert and Bernardo to keep them in the tie, Cole set up a tense final period by halving the deficit.
The Rams appealed in vain for a penalty when Florian Jozefzoon went down under a challenge from Bernardo, before Dan Burn’s poor clearance went straight to ex-LA Galaxy defender Cole for him to head home.
Derby were given four additional minutes to force extra-time but, despite sending keeper Roos up for a late set-piece, were unable to equalise.