Goals from Lewis Dunk and Callum Paterson ensured the two sides were level at the break in south Wales, but the hosts eventually found a way through the Brighton backline after piling on the pressure in the second half.
The early kick-off meant that the 'Bluebirds' had the opportunity to pile the pressure on their relegation rivals with a win, but they made hard work of doing so despite being handed the perfect circumstances.
However, things looked like they could have been a lot worse early on as Dunk celebrated his recent England call-up by heading home Solly March's free-kick from out on the left at the far post with just six minutes on the clock.
Truth be told the visitors looked the better side in the opening exchanges, but they found themselves pegged back just before the half-hour mark thanks in part to a rather large slice of luck.
The impressive Kadeem Harris engaged in a mazy drive into the box before crossing right-footed. There seemed to be no danger, only for a deflection off Gaetan Bong to take out the two covering defenders and present Callum Paterson with an easy header from barely two yards.
The pendulum then swung firmly in the hosts' favour as Dale Stephens was given his marching orders just minutes later as he steamed into a reckless challenge on Greg Cunningham, with Martin Atkinson immediately producing red after seeing the midfielder catch the former Preston man high on the shin.
A series of long-range efforts was all Cardiff could muster before the break, but they threw the kitchen sink at their opponents after the interval, with the pressure eventually telling.
Harris went close to a stunning goal as he rattled the crossbar after cutting onto his left foot, before a barrage of free-kicks, corners and long throws was launched into the Brighton box.
Dunk and defensive partner Shane Duffy were largely immaculate as the likes of Jose Izquierdo, who called Neil Ehteridge into a sharp save with a 20-yard drive, began to threaten on the counter.
Nevertheless, as the game moved into stoppage time Cardiff found the breakthrough, Bamba making amends for losing Dunk for Brighton's goal by following up and firing into the roof of the net after both his and Junior Holiett's efforts crashed back into play off the woodwork.
The win moves Cardiff up to 16th, at least temporarily, whilst Brighton remain 12th.
November 10, 2018