Arsenal kept its five-point lead after 10 games following a stalemate at Goodison Park, which raised doubts about the top-four credentials of both Everton and Tottenham.
The day's other game — played amid a heavy police presence in south Wales — was also heading for a goalless draw when Steven Caulker met Craig Bellamy's corner with a downward header in the 62nd minute, lifting Cardiff above Swansea in the bottom half of the standings.
Swansea was reduced to 10 men in second-half stoppage time when goalkeeper Michel Vorm was given a red card for a professional foul on Fraizer Campbell. With the visitors having used all their substitutes, right back Angel Rangel donned the gloves for the final minutes and was forced into action from the resulting free kick, tipping over Peter Whittingham's effort.
Police were on a high alert for a fixture that has been blighted by fan violence in recent years. In 1993, Swansea fans ripped up seats and threw them at Cardiff supporters in violent scenes that led to the game being referred to as the "Battle of Ninian Park." Visiting fans were banned for the next four years.
Swansea fans had to travel to the match from their home city on special buses that had a police escort — a tactic the police call a "bubble trip." The supporters did not receive their match tickets until they were on board one of the buses.
The contest appeared to pass off without serious trouble — and bragging rights will reside in Cardiff until the return match between the rivals on Feb. 8, thanks to Caulker's meaty header.
Caulker spent a year on loan at Swansea in the 2011-12 season, and didn't celebrate his goal.
"I've always respected the teams I've played for," said Caulker, who joined from Tottenham over the summer. "I'm a Bluebird now and thankful to get the win for us."
Swansea dominated the early exchanges, with Spain forward Michu having two shots saved, but barely threatened after the break.
"It is always easy to brag when you are winning, but there is always a next time," Swansea manager Michael Laudrup said. "You have to remember that — there is always a next time."
With second place up for grabs after defeats on Saturday for Chelsea and Liverpool, the Everton-Tottenham match failed to live up to expectations.
Neither goalkeeper was seriously tested, although Spurs keeper Hugo Lloris was involved in the biggest incident of the match when he was knocked unconscious after his head collided with the knee of Romelu Lukaku in the 77th minute.
After a lengthy spell of treatment, it looked like Lloris was about to be substituted but the France captain chose to play on despite medics advising him to leave the pitch.
"Hugo still doesn't remember the incident with Lukaku so he lost consciousness there but he seemed assertive and determined to continue and showed great character and personality. We decided to keep him on based on that," Tottenham manager Andre Villas-Boas said.
Tottenham jumped two places to fourth and Everton stayed seventh.