Brighton made 11 changes from the weekend's Premier League win over Watford but took a ninth-minute lead at Cardiff.
Enoch Mwepu’s pass dissected the Cardiff defence and Jakub Moder strode clear to finish under the body of Alex Smithies for his first Brighton goal.
Andi Zeqiri doubled a youthful Brighton’s lead at Cardiff 10 minutes into the second half. Taylor Richards found Moises Caicedo and the Ecuadorian laid the ball into the path of Switzerland striker Zeqiri, who swept the ball home in style from just inside the area.
Under 23s Marc Leonard, 19, and Antef Tsoungui, 18, both made their first competitive starts for Albion, while teenagers Andrew Moran and Odel Offiah made their debuts from the bench midway through the second half.
16-year-old Evan Ferguson also made his first outing as an 81st minute replacement for Enock Mwepu.
Under 23's coach Andrew Crofts and player-assistant Gary Dicker were in attendance and would have been pleased with how the younger players performed against an experienced Cardiff outfit.
Albion head coach Graham Potter was delighted with the courage and quality his young team displayed against a physical Cardiff team and also praised striker Zeqiri.
The Swiss attacker has had few chances to shine in the first team but his goal tonight - coupled with injuries to Danny Welbeck and Neal Maupay, plus the departure of Florin Andone - could see Zeqiri feature against Everton in the Premier League this Saturday.
"Yes, absolutely," said Potter. "He is pushing all the time. We know his quality. He has suffered because he hasn't always played in the nine position.
"But he has always been positive. It has not been easy for him for lots of different reasons. He his personality has been excellent.
"Everyone at the club loves him. He's a great kid, always smiling, trying to help the team."
"He knows how much the club think of him and how much I think of him. Whatever situation he is in he always tries his best, which sounds like a given but is not always the case.
"I'm delighted he played as a nine and that he scored."
Potter added: "Really satisfying, very proud of the players. They were fantastic. A young team, they showed courage, had to defend against a strong, physical team.
"Keeping a clean sheet here is not easy."
The third round draw of the Carbao Cup will be held tomorrow night.
Albion: Steele ©, Leonard (Moran 67), Tsoungui, Roberts, Karbownik, Caicedo, Alzate, Richards (Offiah 67), Moder, Zeqiri, Mwepu (Ferguson 81). Subs: Walton, McGill, Furlong.