Tom Ince had the first chance of the match in the 10th minute, but his left-footed shot from the right side of the Norwich box went wide.
Then six minutes later, Norwich opened the scoring through Jonny Howson, who scored from inside the Forest penalty box after being teed up by Russell Martin.
Britt Assombalonga and Michail Antonio came close to equalising for Forest in the latter stages of the first half.
Norwich had a couple of early chances in the second half, before Assombalonga came close for Forest again.
Both sides had chances as the second half progressed but it was Forest who took one of theirs, Assombalonga turning in Matty Fryatt’s cross five minutes from full time.
There was yet more drama to come at City Ground, as Forest scored a late winner. Assombalonga was the architect of the goal as he released Michail Antonio to score in the third minute of injury time.