Two goals from Lucas Perez, a 30-yard strike from Granit Xhaka and a late goal from Alex Oxlade-Chamberlain were enough to put The Gunners through into the next round at a sold-out City Ground.
Head coach Philippe Montanier made three changes from the defeat to Norwich City at the weekend. The Frenchman handed Nicklas Bendtner his first start in a Forest shirt while anther former Gunner Henri Lansbury also made the starting line-up.
Arsenal, as expected, kept the ball well in the opening period of the match retaining possession efficiently. However it was the home side who nearly broke the deadlock twice.
Ben Osborn found Pajtim Kasami on the edge of the area but the Swiss international dragged his shot wide of the far post. Kasami again went close minutes later and perhaps should have done better from inside the visitors' penalty box.
After a mix-up in the Arsenal defence the ball fell to Bendtner who unselfishly squared the ball to an unmarked Kasami. The midfielder had time and space but his effort drifted past the post.
After a sold-out crowd rose to their feet on 12 minutes to pay their respects to former Forest manager Brian Clough, former Reds loanee Chuba Akpom brought out a good save from Vladimir Stojkovic.
The ball was neatly played through to Akpom and his right-footed effort looked to be heading into the top corner, but the Forest keeper managed to get a strong hand to it and push it behind for a corner.
The match was beginning to open up and after Bendtner saw his effort graze the post with a precise curling shot, it was the visitors who went in front on 23 minutes.
Xhaka’s deflected 30-yard effort caught Stojkovic unaware and flew into the top corner despite the Serb getting a hand on it. The goal seemed harsh on the home side who were beginning to look the most likely to score.
The second half started in similar fashion to the first with the visitors dominating possession. The warning signs were there when on 49 minutes when Perez curled a free kick into the arms of Stojkovic after a foul by Cohen.
Ten minutes later the striker went one better to double The Gunners' lead. Michael Mancienne was adjudged to have brought down Akpom in the area and the Spaniard made no mistake from the spot.
The visitors by this stage were brimming with confidence and added a third on 71 minutes through Perez who grabbed his second of the match. The former Deportivo man managed to outmuscle Mancienne and round the keeper to slot home his second and Arsenal's third.
Forest did manage to carve open Arsenal’s defence in the 82nd minute when Lansbury squared the ball to Osborn. Lansbury’s first-time pass found the onrunning Osborn whose half volley went straight at Martinez.
With the final act of the contest, Oxlade-Chamberlain made it 4-0. The England midfielder raced on to a ball through the middle and slotted a left-footed finish past Stojkovic to send Arsenal into round four and leave Forest looking at back-to-back home defeats.
Forest: Stojkovic, Pereira, Mancienne, Mills, Lichaj, Dumitru-Cardoso (Lica 80'), Cohen (c), Lansbury, Kasami (Carayol 68'), Osborn, Bendtner (Vellios 80')
Subs not used: Smith, Fox, Hobbs, Grant
Bookings: Bendtner 16', Lansbury 67', Cohen 75'
Arsenal: Martinez, Maitland-Niles (Bielik 87'), Holding, Gabriel, Gibbs, Oxlade-Chamberlain, Xhaka, Elneny, Akpom (Willock 82'), Reine-Adelaide (Zelalem 82'), Lucas
Subs not used: Macey, Sheaf, Mavididi, Dasilva
Goals: Xhaka 23', Lucas 60' 71', Oxlade-Chamberlain 90'
Bookings: Holding 37'
Referee: Paul Tierney
Attendance: 28,567 (3,617 away)