Forest goalkeeper Stephen Henderson saved Hogan's initial effort and Lewis Macleod's follow-up before Hogan tapped home his first goal of the season.
Dean Smith's Bees have now won back-to-back games at home with clean sheets.
Damien Perquis was sent off late on for Forest for a second yellow card and striker Britt Assombalonga wasted a one-on-one in injury time.
Brentford goalkeeper Daniel Bentley produced a number of second-half saves to secure three points, including his parry from former Southend team-mate Assombalonga.
Earlier, Macleod had hit the crossbar for the Bees while Hildeberto Pereira and Eric Lichaj went close for the visitors.
Head coach Philippe Montanier, who joined Forest in the summer, has seen his team suffer back-to-back Championship losses after their opening day win over Burton.
Brentford boss Dean Smith:
"It was nice to get two clean sheets and two home wins on the spin. We worked very hard for that - you have to in this league because no one will roll over and give you the points.
"We were masters of our own downfall at times because of our decision making and I felt we created most of their chances. People were giving the ball away in the last five or six minutes, but Daniel Bentley was very composed which was just as well.
"We didn't look after the ball well enough in the second half but we defended very well and looked organised, which made it difficult for Forest to create too much themselves. We had to re-organise and I'm glad the players did it themselves rather than me having to do it with substitutions."
Nottingham Forest boss Philippe Montanier:
"We were in control of the game and had many opportunities to score, but the story is always the same. It was a frustrating evening but I was pleased with the character of my side.
"We lacked efficiency to score goals and unfortunately that reflects the whole game. I thought Britt would score late on but we had too many opportunities to score and if you don't there's a danger you can always concede one goal.
"We made mistakes and that is frustrating but the mentality is good and we are trying too hard to achieve victories in what is a difficult moment for us."
Match ends, Brentford 1, Nottingham Forest 0.
Second Half ends, Brentford 1, Nottingham Forest 0.
Attempt saved. Britt Assombalonga (Nottingham Forest) left footed shot from the left side of the box is saved in the centre of the goal. Assisted by Ben Osborn with a through ball.
Apostolos Vellios (Nottingham Forest) wins a free kick in the defensive half.
Foul by Sam Saunders (Brentford).
Foul by Hildeberto Pereira (Nottingham Forest).
Ryan Woods (Brentford) wins a free kick in the defensive half.
Offside, Nottingham Forest. Ben Osborn tries a through ball, but Britt Assombalonga is caught offside.
Attempt saved. Pajtim Kasami (Nottingham Forest) left footed shot from outside the box is saved in the centre of the goal. Assisted by Britt Assombalonga.
Attempt missed. John Egan (Brentford) header from the centre of the box misses to the left. Assisted by Sam Saunders following a set piece situation.
Second yellow card to Damien Perquis (Nottingham Forest) for a bad foul.
Foul by Damien Perquis (Nottingham Forest).
Romaine Sawyers (Brentford) wins a free kick on the right wing.
Pajtim Kasami (Nottingham Forest) wins a free kick in the defensive half.
Foul by Romaine Sawyers (Brentford).
Attempt saved. John Egan (Brentford) header from the centre of the box is saved in the bottom right corner. Assisted by Sam Saunders with a cross.
Corner,  Brentford. Conceded by Hildeberto Pereira.
Hildeberto Pereira (Nottingham Forest) is shown the yellow card.
Offside, Brentford. Scott Hogan tries a through ball, but Romaine Sawyers is caught offside.
Substitution, Brentford. Sam Saunders replaces Lewis MacLeod.
Foul by Apostolos Vellios (Nottingham Forest).
Nico Yennaris (Brentford) wins a free kick in the defensive half.
Offside, Nottingham Forest. Damien Perquis tries a through ball, but Britt Assombalonga is caught offside.
Delay over. They are ready to continue.
Delay in match Callum Elder (Brentford) because of an injury.
Corner,  Nottingham Forest. Conceded by Callum Elder.
Attempt blocked. Ben Osborn (Nottingham Forest) right footed shot from the left side of the box is blocked. Assisted by Oliver Burke.
Corner,  Nottingham Forest. Conceded by Harlee Dean.
Substitution, Nottingham Forest. Britt Assombalonga replaces David Vaughan.
Corner,  Nottingham Forest. Conceded by John Egan.
Ryan Woods (Brentford) is shown the yellow card for a bad foul.
Henri Lansbury (Nottingham Forest) wins a free kick in the defensive half.
Foul by Ryan Woods (Brentford).
John Egan (Brentford) is shown the yellow card for a bad foul.
Oliver Burke (Nottingham Forest) wins a free kick in the attacking half.
Foul by John Egan (Brentford).
Substitution, Nottingham Forest. Oliver Burke replaces Daniel Fox.
Corner,  Nottingham Forest. Conceded by Harlee Dean.
Attempt saved. Hildeberto Pereira (Nottingham Forest) right footed shot from the centre of the box is saved in the centre of the goal.
Eric Lichaj (Nottingham Forest) wins a free kick in the defensive half.
Scott Hogan's goal for Brentford was the difference in their match against Nottingham Forest.