It came after Lewis Dunk celebrated his England call-up with a goal over the bridge in Wales to put the Seagulls ahead - but the visitors eventually succumbed after having to play almost an hour with ten men in the lunchtime Premier League clash.
The Albion captain - fresh from being named in Gareth Southgate's squad for a second time this week - got his side off to the perfect start.
He headed home after just six minutes, before Albion were pegged back in fortuitous fashion midway through the first half when a deflected cross looped up of Gaetan Bong and was headed home by Callum Paterson.
Albion were then forced to play the whole of the second half with ten men against a promoted Cardiff side that started the day second-from bottom in the standings with just five points from their 11 opening games.
Stephens lunged for the ball in a challenge with Greg Cunningham and although he won the ball, his studs caught his opposite number on the shin with the follow through and he was shown a straight red.
The decision divided opinion with pundits and fans on social media, but Martin Atkinson - the man that mattered - deemed it reckless and sent the midfielder off.
City had plenty of the ball in the second half and came close when Kadeem Harris' effort cannoned back off the bar, that was until late pressure when a Bamba overhead hit the post, a follow-up came back off the bar and Bamba turned home the winner as the clocked ticked onto 90 minutes.
Brighton went into the clash having managed just one win in their last 19 Premier League away games, although Chris Hughton was unbeaten in five meetings against Neil Warnock - winning four and with five clean sheets.
Cardiff had failed to score in six of their 11 games this season and also failed to keep a clean sheet in eight league matches.
Albion made two changes with Anthony Knockaert replacing Alireza Jahanbakhsh, who had a slight hamstring strain, on the right wing and Martin Montoya came in for Bruno at right-back.
Jahanbakhsh had started the previous four league matches but limped off late in the defeat at Everton last week, while Bruno has dropped to the bench.
Albion also included under-23 youngster Viktor Gyokeres on the bench while Aaron Connolly also travelled although was not named in the squad.
Cardiff made three changes from their 1-0 loss at home to Leicester last weekend. Cunningham, Joe Ralls and Harris came in for Joe Bennett, Harry Arter and Bobby Decordova-Reid.
Albion got the perfect start as Solly March's free kick to the far post picked an unmarked Dunk, who ghosted in to head across Neil Etheridge and into the bottom corner from four yards out.
The hosts responded by wasting a couple of dangerously-positioned free kicks, while at the other end, March's first-time effort from a Knockaert cut-back was dragged wide.
On 27 minutes, Gaetan Bong's low ball in was met by Glenn Murray and his deflected shot from 12 yards was deflected straight at Etheridge.
Less than a minute later, Cardiff were level. It was a nice bit of build-up play, but a scrappy goal for Albion to concede as a Harris cross from the right skewed up off Bong's thigh and was headed in past a stranded Ryan by Paterson.
Safe hands by Ryan keep the hosts from taking the lead on 31 minutes as Cunningham's half volley looked to be creeping into the top corner.
Soon after Albion were reduced to ten men when Stephens was sent off for a lunging tackle on Cunningham. The Albion midfielder got plenty of the ball and little of his opponents, but referee Martin Atkinson deemed it to be reckless and brandished a straight red.
Paterson was booked for his part in a scuffle afterwards while March, who had started the game well, was sacrificed for Yves Bissouma in an Albion reshuffle.
The visitors held out until the break and while Cardiff started the second half with plenty more of the possession, they failed to trouble Ryan or the Albion back-line until the 59th minute.
A sloppy bit of play on the nearside by Dunk and Bong eventually saw the ball pushed inside to Harris and he took a touch to open up his body, before curling a left-footed effort from the edge of the box onto the face of the crossbar and the loose ball was then put over the bar.
In a rare Albion venture forward, substitute Florin Andone was synically blocked off and from the move the free kick produced a ball in was scrambled clear by Etheridge, only for Jose Izqueirdo to lash high and wide.
The winger then produced a trademark cut-in and shot on 82 minutes that Etheridge did well to push up and over the bar.
At the other end, the visitors withstood some late pressure with Ryan denying Victor Camarasa and two last-gasp blocks to keep them out. That was until a massive goalmouth scramble saw the ball hit the post and the bar, until Bamba put home the winner.
Cardiff: Etheridge; Ecuele Manga, Morrison (Peltier 70), Bamba, Cunningham; Harris, Gunnarsson, Ralls (Decordova-Reid 77), J.Murphy (Hoilett 73); Camarasa; Paterson. Unused subs: Smithies, Bennett, Ward, Damour.
Brighton: Ryan; Montoya, Duffy, Dunk, Bong; Knockaert, Stephens, Kayal, Izquierdo; March (Bissouma 39); Murray (Andone 63). Unused subs: Steele, Balogun, Bernardo, Bruno, Gyokeres.
Referee: Martin Atkinson.