The defender, who spent a season on loan at Swansea, netted just his second Cardiff goal to seal a historic victory for the hosts as their rivals finished the game with 10 men following Michel Vorm's late dismissal.
Cardiff went into the much-anticipated encounter looking to end a run of three games without a win, while Swansea knew that they could move into the top half with maximum points.
Malky Mackay's men were on the back foot for much of the match as Swansea searched for a second successive win at the Cardiff City Stadium.
But it was a former Swansea player who was the difference between the two sides, Caulker scoring a header after 62 minutes.
That proved to be enough for Cardiff, whose task was made easier when goalkeeper Vorm was given his marching orders for a foul on Fraizer Campbell in the dying embers of the game for as the hosts moved ahead of their neighbours.
Cardiff made two changes to the side that drew 0-0 with West Ham last Saturday as Don Cowie and Craig Bellamy replaced Kim Bo-Kyung and Campbell.
Meanwhile, Alvaro was dropped for Swansea, with manager Michael Laudrup bringing Jonjo Shelvey into the starting XI.
Swansea made the better start to proceedings, but saw two promising opportunities wasted as Michu and Jonathan de Guzman both shot hopelessly wide from good areas in the early stages.
The visitors continued to press and forced the first save of the game 10 minutes in, David Marshall keeping out Michu's effort from the edge of the area after the Spain international had evaded the home defence.
Cardiff took 25 minutes to create their first chance, Bellamy's free-kick deflecting wide off Leon Britton.
Swansea dictated the game for large periods but it was Cardiff who began the second half the stronger.
However, they too showed a similar lack of composure in front of goal when Peter Whittingham sliced Bellamy's lay-off well wide four minutes into the half.
The deadlock was finally broken just after the hour mark, though, Caulker rising to head Bellamy's corner past a stranded Vorm.
Laudrup threw substitute Wilfried Bony into the fray immediately after falling behind, and the Ivory Coast international almost had an instant impact as he prodded wide from point-blank range.
De Guzman and Alejandro Pozuelo also went close in the closing stages for Swansea, but any hopes they had of earning a point were virtually ended when Vorm was dismissed after bringing down Campbell after the former Hull City striker had broken through on goal.
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
