It was back to the top of the table for the Gunners after they returned to it with a convincing win over Forest.
Gabriel Martinelli opened the scoring before England's Bukayo Saka was forced to leave the game with an injury.
Four minutes after the restart, Nelson scored his first goal for the club and then added his second.
Two goals from Thomas Partey and one from Martin Odegaard gave the visitors a comfortable victory as they regained their two-point lead over Manchester City at the top of the table.
England fans will be concerned by the sight of Saka heading straight to the tunnel after being taken off, although Mikel Arteta said there was no update on his condition after the match.
Nelson took advantage of his chance to shine on his first league appearance since the opening match of the season.
After Dean Henderson saved his first shot, the 22-year-old put daylight between the teams when he scored at the second attempt.
Nelson scored his second goal in three minutes after poking a Gabriel Jesus cross into the far corner.
Partey struck a superb right-footed shot into Henderson's top corner after Nelson had set him up, and Odegaard completed the scoring.
It was a sobering defeat for Forest, who were basking in the glow of their win overLiverpool.
In the first half, Jesse Lingard's effort was blocked after Gabriel Magalhaes gifted him the ball, and Remo Freuler's long-range shot was picures picures not being seen by the visiting team.
Steve Cooper will be disappointed with the collapse of his side in the early stages of the second half.
It was always going to be difficult for Forest to take something away from the stadium.
They will look to regroup quickly with two home games before the World Cup begins.
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