Second half goals from Ramsey and Giroud ensured Arsenal progressed to the fourth round after the scores were level at the break.
Sunderland had the first half chance of the afternoon on 3 minutes after the ball fell kindly for Watmore, allowing him to play Lens into a threatening position but the Dutchman’s snap shot flew past the post.
Arsenal’s first chance of the game arrived on 9 minutes when Gibbs provided an overlap down the left only to see his shot tipped over by Pickford.
Sunderland made the breakthrough on 17 minutes through Jeremain Lens. A mistake from Koscielny was pounced upon by lens who slammed the ball home at the near post to put the visitors deservedly in front.
Arsenal almost equalised on 22 minutes after Iwobi dribbled past Cattermole, Watmore and Coates before Pickford came out to block his effort.
The gunners did find their equaliser three minutes later after Walcott drove to the by-line before cutting the ball back for Campbell to bury into the corner.
Arsenal dominated early after the break and nearly took the lead on 56 minutes when Oxlade-Chamberlain made space on the edge of the box only to see his curling effort strike the post.
Sunderland straight down the other end had a chance to retake the lead after Yedlin crossed to the back post to find Fletcher who headed off the bar but Watmore’s hurried rebound flew over.
The game was getting very open now and Arsenal nearly capitalised moments later as Campbell played a neat one- two with Oxlade-Chamberlain before finding himself one on one but Pickford made an outstanding save.
Arsenal made their pressure pay as they took the lead on 71 minutes through Aaron Ramsey. Bellerin received the ball in behind Graham before he slid the ball across to the unmarked Ramsey to slot home from close range.
The floodgates seemed to be opening now as Bellerin yet again found space down the right before finding Giroud at the back post who tucked the ball past Pickford.
Sunderland weren’t giving up easily and Danny Graham had a chance to pull a goal back on 78 minutes when he was played through on goal but Cech came out fast to make the save.
Arsenal (4-2-3-1): Cech, Bellerin, Gabriel, Koscielny, Gibbs, Chambers (Arteta 66’), Oxlade-Chamberlain, Iwobi (Ramsey 66’), Walcott, Campbell (Reine –Adelade 81’), Giroud.
Subs: Macey, Debuchy, Arteta, Ramsey, Monreal, Reine-Adelade, Willock.
Goals: Campbell (25’) Ramsey (71’) Giroud (75’)
Sunderland (4-3-3): Pickford, Van Aanholt, Yedlin, O’Shea (c) (Jones 65’), Coates, Cattermole (M’Vila 57’), Toivonen, Lens, Watmore, Fletcher (Mavrias 76’), Graham.
Subs: Mannone, Jones, Beadling, M’Vila, Mavrias, Borini, Defoe
Goals: Lens (17’)