The breakthrough came in the 29th minute of the contest, and Forest were unable to find a leveller despite their best efforts, with the Reds staying down in 17th position in the table, three points above 18th-placed Luton Town, who have a game in hand.
Brighton, meanwhile, have moved into seventh position, with the Seagulls five points behind sixth-placed Manchester United on the same number of games (28).
Both sides entered the match off the back of three straight losses, with Brighton going down 4-0 to Roma in the first leg of their last-16 Europa League contest on Thursday, but Roberto De Zerbi's side were able to bounce back with an unconvincing win.
The first opportunity of the match came for Brighton in the 10th minute, but Simon Adingra's effort never had the power or direction to beat Matz Sels between the Forest sticks.
The Seagulls had another half-chance less than a minute later through Carlos Baleba, but his effort flew wide of the post, with the home side starting to step up the pace after a quiet start to the contest.
Selz was again called into action in the 16th minute to keep out a header from Jakub Moder, and it was very much one-way traffic at the Amex, with Forest struggling to make their mark.
Some strong defending from the visitors prevented a shot from Ansu Fati potentially landing in the back of the net in the 20th minute, before Adingra fired over the crossbar from a half-cleared corner shortly after.
Evan Ferguson came close to meeting a cross from Adingra in the 26th minute, as Forest survived again, but the breakthrough did come in the 29th minute of the contest.
A brilliant corner from Pascal Gross caused all sorts of problems inside the Forest box, and there was initially confusion over who had got the final touch, but it was later confirmed to be an own goal from Omobamidele.
The visitors believed that there was a foul on their goalkeeper, but the referee was happy for the goal to be awarded and VAR agreed.
Forest had opportunities to hit back in the period that followed, but Divock Origi saw his strike kept out by Brighton goalkeeper Bart Verbruggen, before Morgan Gibbs-White dragged an effort wide of the post, and the home side entered the half-time break with a one-goal advantage.
The visitors were on the front foot at the start of the second period, with Origi having another chance in the 47th minute, but his effort following a flick from Gibbs-White was always missing the target.
Brighton goalkeeper Verbruggen was then called into action to keep out an effort from Murillo, before Selz did well to save a powerful drive from Fati down the other end of the field.
Chris Wood came close to levelling the scores in the 70th minute, but the Forest striker's effort from a tight angle was kept out by the home side's goalkeeper.
Verbruggen was again called into action in the 78th minute to keep out a free kick from Gibbs-White, with Forest throwing everything at the hosts in an attempt to level the scores, and Cheikhou Kouyate headed over the Brighton crossbar in the latter stages of normal time.
Six additional minutes were added at the Amex, but Forest were unable to score a leveller, with the Reds losing for the 16th time in the Premier League this season.