The Bluebirds dominated their first round tie against Brighton played in front of just 3,726 at Ninian Park.
Despite having their fair share of possession they struggled to break down a resilient Brighton defence.
But with penalties looming, defender Johnson headed home a Cardiff corner to give them a lead they never looked like surrendering.
Cardiff manager Dave Jones
"These are always difficult games, we found that out last season and tonight was about finding a way to break them down.
"I think Brighton deserve a lot of credit for the way they defended. They made it difficult for us and things aren't happening for us up front.
"But credit to my strikers they didn't shy away from the challenge and kept on plugging away and generally it was a tough game and I'm pleased to have won.
"We know it is an area that we need to strengthen and I am looking to add another striker to that department because we are short of strikers."
Cardiff: Turnbull, Capaldi, Purse, Johnson, Gunter, Rae, Whittingham (Ledley 78), McPhail, Parry (Ramsey 116), Feeney (Green 65), MacLean. Subs Not Used: Oakes, McNaughton.
Goals: Johnson 110.
Brighton: Kuipers, Whing, Lynch (Rents 46), Butters, El-Abd, Elphick, Fraser (Reid 73), Hammond, Cox, Revell (Savage 106), Forster. Subs Not Used: Sullivan, Elder.
Booked: El-Abd, Cox, Forster.
After Extra Time
Ref: T M Kettle (Rutland).