The Reds were awarded all three points thanks to a goal by Taiwo Awoniyi in stoppage time in the first half, but the contest was not without controversy.
VAR was used multiple times, as both teams had goals disallowed, and Forest worked extremely hard for their win.
Here are four things that we learned on Sunday.
Dean Henderson impressed in front of Gareth Southgate
The Forest goalkeeper will be pleased that he was able to put in an outstanding performance while the England manager was present.
Henderson has made several impressive saves so far in his short time at Forest, and some of the saves he made against West Ham were particularly eye-catching.
During his team's victory, Henderson completed four saves, four high claims, two clearances, and seven long balls.
Neco Williams looks to be the perfect Djed Spence replacement
The Welsh international had the most touches (76) and completed the most duels (9), tackles (6), and successful take-ons (2) of any outfield Forest player.
The 21-year-old also had the most shots in the game (4) and created the most chances (2) for Forest.
It was critical for Forest to sign a right wing-back who could defend confidently while also attacking enough to pose a real threat, and Williams has demonstrated both abilities in his second game in red.
From Trent Alexander-Arnold-esque passing to goal line clearances, Williams delivered an all-around wing-back performance that his new manager, as well as Forest fans, will be pleased with.
Benrahma a shining light on a miserable afternoon for West Ham
Although occasionally unreliable, the forward proved his value against Forest. He appeared sharp the entire match and was direct and speed pacy.
Prior to his thundering free-kick hitting the woodwork, the Algerian caused Dean Henderson to make a significant save and even had a goal disallowed.
Benrahma presented a significant threat to Forest's back line during the game by completing four dribbles and recording four key passes. The 27-year-old contributed on defence as well, winning seven ground duels.
Before this game, the Hammers might have been open to offers, but Benrahma's performance proved that he will be helpful to the teams' pursuit of Europe this year, even if it is from the bench.
A quiet day for Jarrod Bowen
The attacker didn't pose any problems for Forest at all, despite having 22 goal involvements in the Premier League last season.
Bowen misplaced all five of his attempted crosses and lost possession of the ball 15 times.
Only 15 of his passes were successful during the whole game, and the 25-year-old failed to get a shot on goal or create any significant chances.
The attacker put on a similar display against Manchester City, and while that can be expected against the league champions, Bowen will need to be at the top of his game to help West Ham qualify for Europe once more this year.