Having beaten them on home soil last season, the Swans secured a shock 2-0 victory at the Emirates Stadium last month, and were hoping that they could repeat the feat in Wales.
Despite taking the lead in the match through Michu, Swansea were forced to find a late equaliser from Danny Graham and snatch a 2-2 draw, after a quick-fire double from Lukas Podolski and Kieran Gibbs had put the Arsenal in front.
Both sides will be now go into the hat for the fourth round of the competition, and will undergo a replay at the Emirates Stadium, with the winner travelling to Brighton & Hove Albion.
Here, Sports Mole decides if either side could argue that they deserved to have progressed through to round four at the first time of asking.
On target 5
On target 9
Was the result fair?
Arsenal were probably the better side throughout the 90 minutes, but a defeat for Swansea would have been harsh. Neither side deserved to lose what proved to be an exciting cup tie, and they will now have to do battle once again at the Emirates Stadium.
Swansea City's performance
The Swans were mainly playing on the counter-attack and to some effect. They didn't control much of the game, although they did have their spells of superiority. They always looked dangerous on the break, and put in a very commendable display against a strong Arsenal team.
The Gunners will certainly be frustrated not to have won here. They controlled large periods of the match, but failed to take their chances, which could have put them out of sight. As much as you can commend Arsenal for coming from behind to go in front, you should criticise them the same amount for letting their lead slip with poor defending.
Sports Mole's man of the match
Michu: It is very tough to give this award to one player today, as several players could be given the honour. However, Michu turned the game when he was brought on, instantly putting Swansea ahead with a brilliant solo effort before terrorising the Arsenal backline for the remainder of the match. What a season he is having, as he takes his goal tally to 15 for the campaign.
In what was a fast and frantic game at times, Howard Webb did very well to keep everything in order. He correctly denied Aaron Ramsey a penalty, after the Welshman tripped himself up inside the Swansea box, and dished out a few yellow cards where necessary.
Swansea City: Swansea travel to Everton in the Premier League on Saturday, before facing the Gunners in the replay of this fixture on January 16.
Arsenal: The Gunners face a real tough schedule for the remainder of January, starting with a match against Manchester City next weekend.