Both clubs have changed managers since Cardiff beat Swansea in their first-ever top flight meeting in November, but Swansea caretaker-manager Garry Monk was far happier after his first match in charge than Cardiff's Ole Gunnar Solskjaer.
The match at the Liberty Stadium tilted Swansea's way when Pablo Hernandez replaced the injured Marvin Emnes at halftime and set up the opening goal two minutes into the second half.
His raking pass found Wayne Routledge, who once had a spell on loan at Cardiff, and he curled home with a close range effort.
The defeat left Cardiff, in the top flight for the first time in 51 years, second from bottom, two points clear of Fulham.
Monk, 34, who took over as caretaker following Laudrup's departure on Tuesday, played almost 256 games for Swansea before announcing his retirement as a player on Thursday.
He told Sky Sports he was excited because he knew exactly what the result meant for the fans.
"I have played in a lot of these matches and know what it means. But I had to keep calm and keep a clear head on the touchline but I am delighted.
"The result was the reward for all the hard work we have put in this week and what I tried to put across to them. The players were magnificent today."
Solskjaer, who has only won one league match and lost four since taking over from Malky Mackay in January, said he was pleased with Cardiff's first-half performance and there was hope for the rest of the season.
"I am bitterly disappointed and it hurts a lot for me and the players and the fans of course and now they move six points ahead of us but with a win we would have been the same as them.
"Now we play Aston Villa in three days' time. We will have the supporters with us, and I am sure we will be fine."
- Sports & Recreation
- Ole Gunnar Solskjaer
- Wayne Routledge