The two sides could not be separated at the Liberty Stadium earlier this month after Danny Graham snatched the Swans a 2-2 draw to force another battle for progression at the Emirates.
In what proved to be a very one-sided encounter, Arsenal earned a 1-0 victory through a late Jack Wilshere strike and will now travel to Championship side Brighton & Hove Albion in the fourth round.
Here, Sports Mole decides if it was a fair result in North London.
On target 16
On target 1
Was the result fair?
Without a doubt. Arsenal were the better side in the first half, and absolutely dominated the second half. It seemed like it was going to be one of those days for the club as the game wore on, with the Gunners failing to find the back of the net. You always felt as well that Swansea could cause trouble on the break. However, Wilshere slammed in the winning goal late on to give Arsenal the win they deserved.
Despite a bit of a lull during the midway point of the first half, the Gunners started the brighter of the two sides, and dominated the vast majority of the clash. They looked as if they might have been punished for their poor finishing, as they failed to make the most of their chances. They came out for the second half more clinical, and were finally rewarded for their domination when Wilshere netted the winner three minutes from time.
Swansea City's performance
Swansea never really got into the game, and were limited to very few chances. They weren't battered as far as possession was concerned, but they rarely had the ball in the Arsenal half, and failed to test Wojciech Szczesny too much. The Swans seemed to be saving themselves for other competitions, and lost to the far better side.
Sports Mole's man of the match
Jack Wilshere: While Kieran Gibbs deserves a mention, Wilshere was a class apart from everyone else on the pitch tonight. He seems to be the complete package; agile, elegant and intelligent on the ball yet energetic, determined and not afraid to get stuck in when not in possession. He fully deserved to score the winner, and it was a great goal at that. Fantastic from Arsenal's number 10.
Mark Clattenburg didn't really have too much to do tonight, apart from blow the whistle to award Arsenal a corner or Swansea a goal kick. He didn't hand out a single yellow card, and did not have to make any real tough decisions. An easy night for any referee.
Arsenal: The Gunners are currently in the middle of a difficult run of games, and it gets no easier as they travel to Stamford Bridge to face Chelsea in the Premier League on Sunday.
Swansea City: The Swans are back on home turf in Saturday, when they welcome Stoke City to the Liberty Stadium.