The game failed to live up to the hyped build-up, with few chances at either end at Cardiff City Stadium.
Michu missed Swansea's best opportunity in just the fifth minute, but it was Cardiff who emerged 1-0 winners as Caulker, who spent a season on loan at Swansea, rose to score the winner.
Swansea, who had goalkeeper Michel Vorm sent off in stoppage time, had started the game strongly, but Michael Laudrup's side gradually faded as Cardiff came on strong in the second half.
And all the recent furore caused by Iain Moody's removal as head of recruitment, the uncertainty over manager Malky Mackay's future and the motives of owner Vincent Tan will be briefly forgotten as Bluebirds' fans revel in derby glory.
Swansea had looked to control possession amid the deafening noise of the opening exchanges, and they carved out a great opportunity in just the fifth minute.
Michu brilliantly controlled Jonjo Shelvey's cross but, having done the hard part, volleyed well over the bar.
The Spaniard then warmed David Marshall's hands from distance as Swansea started with the greater authority.
The expected on-field hostilities soon arrived as Angel Rangel and Craig Bellamy exchanged words as it took Cardiff time to settle, but Ben Turner's strong challenge on Shelvey sparked a gradual change in proceedings.
As predicted Cardiff threatened at set-pieces, and Leon Britton came uncomfortably close to diverting a Bellamy free-kick into his own net.
A couple of pin-point dead-ball deliveries from Peter Whittingham forced Vorm to punch unconvincingly and, as Cardiff got a foothold in midfield, the action dried up.
Swansea enjoyed the better of possession, but Cardiff were comfortably able to soak it up, while reluctant to press on in attack and the arrival of the half-time whistle was almost merciful.
There was at least a modicum of action early in the second half. Peter Odemwingie narrowly failed to connect with a Caulker flick-on, before Whittingham drove wide following a purposeful surge from Kevin Theophile-Catherine.
The Bluebirds had half-hearted penalty appeals for a foul on Don Cowie by Ashley Williams turned away by Mike Dean, refereeing in the Welsh capital for the first time since being struck by a coin in this fixture over four years ago.
But they got their reward for their strong start to the second half in the 62nd minute, and it was Caulker who stung his former club.
The England defender rose above Chico Flores, the man Swansea signed to replace him following the end of his loan spell at the Liberty Stadium, to powerfully head home a Bellamy corner.
Michu had been signalling throughout the passage of play that he was carrying an injury, and skipper Williams appeared to let the bench know in no uncertain terms a replacement should have been readied as his side effectively played with a passenger.
Caulker then made a telling contribution at the other end, bravely getting in to deny substitute Wilfried Bony, on for the injured Michu, tapping in an equaliser from Jonathan de Guzman's header back across goal.
But the goal had clearly stunned Swansea, and their confidence seemed to evaporate as a hungry Cardiff tore at them, with Vorm twice saving from substitute Fraizer Campbell.
Marshall saved a sharp Vazquez effort as the game entered five minutes of stoppage time, and Swansea's misery was completed when Vorm saw red after racing from his area and clattering Campbell, leaving Dean with little choice.
With all of their substitutes used, Swansea had to throw Rangel into the goal for what time remained but Cardiff were unable to add to their tally.
Source: PA
Source: PA