Goals from Joel Campbell, Aaron Ramsey and Olivier Giroud were enough for the Gunners after Sunderland took a surprise lead through Jeremain Lens.
Gunners manager Arsene Wenger made a few changes from the team that recently beat Newcastle United, resting key midfielders Ramsey and Mesut Ozil, with Alex Iwobi and Alex Oxlade-Chamberlain promoted to the starting XI.
The Black Cats also made several changes as coach Sam Allardyce rotated his options, selecting goalkeeper Jordan Pickford, DeAndre Yedlin and Sebastian Coates for duty.
Arsenal tested Pickford in the opening moments of the contest, but it was Sunderland that struck first after a horrendous mistake by Laurent Koscielny.
The Frenchman was robbed by Lens after a back-pass from Kieran Gibbs, and the Sunderland midfield buried his chance past 'keeper Petr Cech after 17 minutes.
Bleacher Report's James McNicholas called the action:
1-0 to Sunderland, Lens strikes after an error from captain Koscielny. Gibbs did him few favours but he ought to have cleared his lines.2016-1-9 15:17:35
Sports Illustrated blogger Blake Thomsen mused a cup exit would not be the worst outcome for Arsenal:
Blake Thomsen @blakecthomsen
70 minutes to recover, but losing this is probably the best thing for Arsenal. If you're not gonna win whole thing, may as well lose early.2016-1-9 15:23:54
The hosts immediately responded, as Theo Walcott looked to penetrate from the left. It took Wenger's men just eight minutes to reply through Campbell, who finished in style.
Walcott sprinted through the inside channel for the Gunners, and his cross was met by Campbell, who ghosted into position in the penalty area and slotted away with ease.
OptaJoe highlighted an upturn in form for the goal hero:
2 - Joel Campbell has scored two goals in his last three starts for Arsenal at the Emirates - both vs Sunderland. Familiar.2016-1-9 15:28:30
Squawka mentioned Arsenal's fantastic record in the domestic cup:
Squawka Football @Squawka
Arsenal have now scored in 21 of their last 22 FA Cup home ties. Prolific record in this competition. https://t.co/idAiZpyCQl2016-1-9 15:41:31
Oxlade-Chamberlain and Campbell both continued to menace the Sunderland defence, but Wenger's side was clearly missing the world-class influence of Ozil.
The Black Cats held their own late into the half but were sinking deeper into their box as the hosts chased a second goal before the break.
Sunderland survived a late onslaught from the Gunners, with the scores level at the half-time whistle.
Guardian sports writer Barney Ronay was not impressed with the position Calum Chambers took up during the opening 45 minutes:
Barney Ronay @barneyronay
Calum Chambers in central midfield? Not for me Clive2016-1-9 15:39:45
There was further criticism from journalist Piers Morgan, who questioned striker Giroud's performance:
Piers Morgan @piersmorgan
Giroud has been a complete waste of Gallic space today. #afc2016-1-9 16:11:20
The Gunners almost took the lead in the opening minutes of the second half, as Campbell had a goal-bound flick cleared. This was soon followed up by a curling effort from Oxlade-Chamberlain, who struck the post with his shot.
However, the pressure motivated the visitors to attack, as Yedlin's excellent cross was headed against the bar by Steven Fletcher with Cech well beaten.
The match began to adopt a real cup atmosphere as possession swung back and forth. The Gunners finally took control of the tie as Ramsey made an immediate impact from the bench after coming on as a substitute. The Welshman finished with aplomb in the 72nd minute, latching on to a Hector Bellerin cross.
The tie was put to bed just three minutes later as Giroud made up for a quiet performance. Bellerin was once again the creator, leaving the striker with a tap-in to make it 3-1.
Morgan was delighted Giroud arrived at the party:
Piers Morgan @piersmorgan
BOOOM! 3-1. Giroud finally responds to my motivational tweets. #afc2016-1-9 16:34:31
At the end, it was a comfortable 3-1 win for the Gunners, but Sunderland were worthy opponents.
The Black Cats battled deep into the match, as Allardyce drove his team forward, but Arsenal's class was too much.
Wenger will feel his team can once again excel in this competition as the north London outfit look to retain the trophy.
Wenger was satisfied with his team's comeback on Saturday and spoke about his desire to bag yet another FA Cup trophy, per the club's official Twitter account:
Arsenal FC @Arsenal
Wenger: "In the second half we took over and played in there half. We scored three fantastic goals." #AFCvSFC2016-1-9 17:18:10
Arsenal FC @Arsenal
Boss on a third FA Cup win: "We are only one trophy away. We have a great desire to do well." #AFCvSFC2016-1-9 17:18:46
The Gunners progressed to the fourth round of the competition, as they hope to win the cup for a third consecutive campaign.