The result was enough to see Cardiff move above Swansea into 13th place in the Premier League table.
Read Sports Mole's minute-by-minute report below to find out how the action unfolded.
3.01pmHello there and welcome to Sports Mole's live text coverage as Cardiff City play host to rivals Swansea City in the Premier League. What a tasty encounter this promises to be.
3.03pmWe should have some team news filtering through at any moment. We'll bring it to you as soon as it does.
3.06pmThere's also another match being played in the Premier League at the moment as Everton host Tottenham Hotspur. The game is currently goalless with around 10 minutes left in that one at Goodison Park. We'll update you with the score as soon as the full-time whistle goes.
3.17pmJust the one change for Swansea after last weekend's goalless draw with West Ham as Jonjo Shelvey replaces Alvaro Vasquez.
3.20pmToday is an historic day for Welsh football as these two teams meet in the top flight for the first time. It's the sort of fixture that is tantalising to say the least, with both teams expected to bring plenty of passion to the capital.
3.23pmHowever, it is safe to say that there is a huge police presence around the Cardiff City Stadium due to the tensions between the two clubs. Let's hope that we just get a decent match with no trouble off the pitch.
3.25pmIn an interesting twist of fate, today's referee is Mike Dean. The 45-year-old was in charge the last time that the teams played each other in February 2011, but was struck on the head by a coin thrown from the stands during that clash.
3.29pmUPDATE: The full-time whistle has just blown at Goodison Park, with Everton and Tottenham Hotspur sharing the spoils in a 0-0 draw. There was a whopping nine minutes of injury time played in that one after Spurs goalkeeper Hugo Lloris suffered a head injury, though he was able to play on.
3.32pmAnyway, back to business. Cardiff are in need of the points near the bottom of the table, and a win today would see them move four points clear of the drop zone. Meanwhile, victory for Swansea would lift the visitors into the top half of the table.
3.48pmNeedless to say, the Cardiff City Stadium is filling up nicely. The home fans are already in fine voice, but there's also plenty of Swansea supporters here as well. Just over 10 minutes until this one gets underway.
3.52pmFormer Cardiff City striker Robert Earnshaw tells Sky Sports News: "[The rivalry] is bitter. It cuts very, very deep."
3.55pmThe players are in the tunnel waiting to step out into the cauldron that is the Cardiff City Stadium. The place is going to explode when the teams emerge.
3.57pmThe teams exit the tunnel, and what a reception from inside the Cardiff City Stadium. It's electric!
1 minThe pre-match rituals have been completed and it will be Swansea to get us underway. Hold onto your hats, here we go!
3 minDespite the tremendous chorus of boos ringing around the stadium, Swansea have shown plenty of composure during the opening few minutes. They're looking to play their trademark passing game early on.
4 minCHANCE! What a glorious opening for Swansea to take the lead! Shelvey's cross was beautifully controlled by Michu, but the Spaniard could only blast his effort over the crossbar from around 12 yards.
7 minCardiff are starting to find their feet a bit more now. Nothing fancy, just making sure that everyone gets a touch. Not quite the frantic opening to this match as predicted, though there's plenty of fire out there on the pitch.
9 minSAVE! Another decent chance falls Michu's way as he unleashes a powerful strike from the edge of the box, but Marshall is able to push the ball away from danger. The visitors are on top.
14 minIf anyone looks like getting the opening goal at the moment it's Swansea. Cardiff are starting to enjoy a bit more possession, but they haven't really done anything with it in terms of the final third.
16 minThere's a little bit of tension between Bellamy and Rangel right now. Both players have been involved in a couple of exchanges, with Mike Dean having a word with the latter to try to calm things down.
19 minSomething of a half-chance for Cardiff as Caulker's header back across goal is met by Whittingham, but the midfielder can only nod wide while under the attention of about three Swansea players.
22 minBoth teams are showing plenty of attacking intent at the moment, though there's a real lack of quality when either side makes it into an advanced position. Still goalless.
25 minCHANCE! Close for Cardiff as Bellamy's free kick from all of 30 yards flies narrowly over the crossbar courtesy of a deflection. Whittingham takes the resulting corner, but Swansea clear their lines.
28 minIt must be said that Mike Dean has officiated this match superbly so far. There have been one or two little incidents between the opposing players, though the man in the middle has done well to calm down any flashpoints.
32 minThe game has become a bit disjointed in the last few minutes, with both teams guilty of giving away possession too easily. However, the momentum seems to be with Swansea. The visitors continue to probe, but the Cardiff defence is standing firm.
35 minNot sure if that was an attempt on goal from Swansea captain Williams as he appeared to try to lob Marshall in the Cardiff goal. It was an easy catch for the shotstopper, though.
39 minIt's all currently a bit tense out there on the pitch. Neither team is showing that much invention in attack, making for a bit of a dull spectacle. This game started with a lot of promise, but it hasn't lived up to it so far.
40 minFive minutes left of normal time in the half.
43 minCardiff are struggling to get out of their own half as the opening 45 minutes nears its conclusion. Swansea are probing around the opposition penalty area, but to no avail as yet. If the home side are going to make the breakthrough it will most likely be on the break.
45 minOne minute added time at the end of this first half.
4.48pmReferee Mike Dean blows the half-time whistle, with the game goalless between Cardiff City and Swansea City. Not a classic opening 45 minutes, it has to be said.
4.51pmSwansea had the better of that first half, but they struggled to really carve Cardiff open. Michu missed a good opportunity early on, while the Spaniard saw a later effort saved by David Marshall. Meanwhile, Cardiff failed to create any clear-cut chances.
4.58pmWe've already had one full-time result in the Premier League today as Everton and Tottenham played out a goalless draw at Goodison Park. You can reach our match report of that one here.
46 minThe players are back out and it will be Cardiff to kick us off for this second half. Here's hoping it's more entertaining than the first.
49 minBoth teams have started where they left off in the first half, with little space on offer across the pitch. Swansea have a sniff of a chance when Shelvey heads down a cross in the Cardiff box, but the home defence hoof the ball clear.
50 minCHANCE! Bellamy tees up Whittingham on the edge of the box, though the midfielder can only blaze his effort high and wide. That was probably the hosts' best opportunity of the match from open play.
52 minPENALTY APPEAL! Cardiff want a penalty as Cowie goes down while battling for an aerial ball with Williams, but Mike Dean waves away the protests. It would have been a harsh one had he given it.
53 minSUBSTITUTION: Cardiff make the first change of the match as Aron Gunnarsson replaces Jordan Mutch.
58 minThere's a little bit more bite to this second half, with Cardiff doing most of the pressing. However, we're still yet to see a goal. This is much better from the home side, though.
61 minCardiff lead and it's Steven Caulker with the goal! The defender, who used to play for Swansea, rose highest to head in Bellamy's corner. Simple but effective for the home side.
64 minSUBSTITUTION: Swansea make a change now as Wilfried Bony comes on for Michu. The Spaniard looks to be struggling with an ankle knock.
66 minAs you can imagine, that goal has brought the Cardiff fans to life. There's a rocking atmosphere inside the ground now after a quiet opening to the second half.
68 minCHANCE! Nearly an equaliser for Swansea as Bony got on the end of Routledge's knockdown, but the striker could only poke wide from close range with Caulker breathing down his neck.
70 minSUBSTITUTION: Twenty minutes left of normal time at the Cardiff City Stadium. Can Swansea salvage something from this match? They're making another change now as Alejandro Pozuelo replaces Leon Britton.
74 minSUBSTITUTION: Another swap for Cardiff here, with Fraizer Campbell coming on for Peter Odemwingie.
78 minTime is swiftly running out for Swansea, who do not look like getting an equaliser anytime soon. If anything, Cardiff have been buoyed by their goal and are working even harder now. They're first to every ball, which is keeping the fans happy as the rain starts to fall.
81 minSUBSTITUTION: Wayne Routledge's afternoon is over as he is replaced by Alvaro Vasquez. Under 10 minutes remaining at the Cardiff City Stadium. It's sure to get more tense as we enter the final stages.
85 minYELLOW CARD: We have the first booking of the match! It's Peter Whittingham who gets cautioned for chopping down Chico.
87 minSUBSTITUTION: Cardiff's final change of the match sees Kim Bo-Kyung on in place of Gary Medel.
89 minSAVE! Not the best stop from Marshall, but it will do! The Cardiff goalkeeper got down to push away De Guzman's free kick, which skipped off the wet turf.
90 minFive minutes of added time. Can Cardiff hold on?
90+1 minNow then! Swansea goalkeeper Michel Vorm is shown a straight red card for bringing down Campbell with the Cardiff striker through on goal. The visitors have made all of their substitutions, so it will be Angel Rangel to go between the sticks for the final few minutes.
90+3 minSAVE! Rangel is forced into action instantly as he pushes Whittingham's free kick over the bar. Not a bad bit of goalkeeping, to be fair.
5.55pmMike Dean blows the final whistle and there is jubilation for Cardiff City as they beat local rivals Swansea City 1-0 thanks to Steven Caulker's 61st-minute header. It wasn't a cracker, but the Cardiff players and fans will not care one jot.
5.57pmAnyway, that's all from me for now but don't forget that you can keep up to date with all of the reaction from the game right here on Sports Mole. Thanks for your company and we hope to see you again soon. Enjoy the rest of your weekend and goodbye!