PHOTO: AFP
Neil Warnock's side would have been pushed to the brink of relegation with a defeat at the Amex Stadium.
But goals either side of half-time from Nathaniel Mendez-Laing and Sean Morrison moved third-bottom Cardiff to within two points of fourth-bottom Brighton.
Brighton have managed just two top-flight goals at home in 2019 and a fourth successive league loss keeps them in danger of being overhauled by Cardiff.
The remaining hope for Brighton is they have five games to play compared to Cardiff's four.
Albion face Tottenham, Arsenal and champions Manchester City during a tough run-in.
With Liverpool and Manchester United still to come this season, anything but a win would have been disastrous for Cardiff.
"We had a few pundits say it would be our final game in the Premier League but we are alive and kicking," Warnock said. "We deserved tonight. I can't say anything better about the players. They have been great for me. We came out of the traps and enjoyed it. We are far from finished yet."
Albion boss Chris Hughton added: "It's still in our hands, but it is a difficult feeling because of the result.
"My job is to lift spirits. This is a proper fight. We have to make sure we turn it round by staying together, digging deep and making ourselves hard to beat."
Solly March had rippled the side-netting inside two minutes for Brighton.
Referee Andre Marriner waved away penalty appeals when Lewis Dunk was wrestled to the ground by Bruno Ecuele Manga following a Pascal Gross free-kick.
But Warnock's decision to recall Mendez-Laing was rewarded in the 22nd minute when he drove forward on the counter-attack, exchanged passes with Junior Hoilett and curled a superb strike into the top corner from 20 yards.
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