Ben Wilmot’s first half goal was enough to give three points to Steve Cooper’s side as they moved two points behind West Brom at the top of the table.
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This was the first south Wales derby since February 2014 when Garry Monk marked his first game as Swansea manager with a 3-0 win over Ole Gunnar Solskjaer’s Cardiff.
Nathan Dyer and Wayne Routledge were among the scorers that day, and the pair both started as Swansea boss Cooper made six changes in an attempt to arrest a run of poor form.
Swansea had picked up only one point from four home games, while Cardiff were also short on wins with two from their previous 10 outings.
Sean Morrison saw his early near-post effort gathered, but the captain gave Cardiff concern when he fell awkwardly and needed lengthy treatment on a wrist injury.
Swansea quickly settled into their passing rhythm with Matt Grimes and George Byers shining in midfield and Andre Ayew relishing his lone-striker role.
Ayew raced onto a 10th-minute through ball from Byers and Cardiff were grateful to Lee Peltier’s goal-line intervention.
Bersant Celina almost punished goalkeeper Neil Etheridge’s poor clearance from inside his own half and Grimes fired over from 20 yards as Swansea continued to press.
The pressure was rewarded after 24 minutes when Swansea worked a short-corner routine and Routledge crossed for the unmarked Wilmot to power his header home.