The centre-back rose to nod Stephen McPhail's 110th minute corner into the back of the net to hand the Bluebirds a 1-0 win in a tepid affair at Ninian Park
The game always seemed destined to go the distance as the home side lacked class and often resorted to shooting from range.
Cardiff enjoyed the best of the early exchanges but failed to make the most of their possession with only a deflected Steven MacLean shot calling Brighton keeper Michels Kuipers into action.
A rasping effort from Paul Parry stung the keeper's hand after 25 minutes but the Seagulls stopper managed to get the ball before the lurking Warren Feeney could pounce.
Brighton did not threaten the Cardiff goal until late on in the first half when defender Tommy Elphick sent a 25-yard shot just wide of Ross Turnbull.
And after a lacklustre 45 minutes, things failed to improve for either side in the second period.
Cardiff always seemed in control but lacked the cutting edge leaving the Seagulls to almost snatch an unlikely lead on the hour mark with a long-range curler from Dean Cox just creeping past Turnbull's post.
Feeney nearly opened the scoring after 65 minutes as he picked up the ball on the edge of the Brighton box and created space, but his deflected shot only clipped the outside of the post
That was the last real chance of a turgid 90 minutes and the game petered out with both sides seeming to accept the inevitable extra time.
McPhail went close for the home side in the additional 30 minutes, but it looked like the game was set for penalties before Johnson broke free at the back post and headed the Bluebirds into the second round.