They were the better side throughout the game and thoroughly deserve their place in round four, where they will face holders Leicester in a derby clash.
Arsenal, on the other hand, were alarmingly off the pace and their performance was summed up by the fact that they failed to muster a single shot on target.
Mikel Arteta’s side just never got going and, ahead of a trip to Anfield on Thursday, this was a worrying display.
Left-back Nuno Tavares was hooked after 35 minutes, such was his poor performance, but in truth he was just the worst of a very lacklustre team. By the end of the match, other than Bernd Leno, no one from the Arsenal side could really hold their heads high.
In the first half the Gunners had plenty of possession, around 60 per cent, but they couldn’t create anything. The fact Ben White had their best chances, dragging a shot wide and being pulled down for a penalty shout, summed up the display.
The second half wasn’t much better and, when Arsenal finally created something, Eddie Nketiah could only head harmlessly wide after Bukayo Saka had picked him out.
Arteta was getting more and more animated on the touchline as the game went on, but the performance stayed flat throughout the 90 minutes. The passing was sloppy and, eventually, Forest got the winner they deserved.
The hosts won the ball in midfield and pounced down the right, with Grabban sliding in to score at the back post.