Paul Gerrard's early penalty save from Leon Knight ensured only their second clean sheet of the season on their travels.
But new boss Gary Megson was left to reflect on a number of missed chances as Brighton maintained the 12-point gap between the teams.
Gerrard went from villain to hero after flattening Knight inside his own area. The former Everton keeper dived full length to keep out the penalty from Knight, who also had a spot-kick saved at Milwall last month.
Forest, hesitant early on, improved after that let-off with Andy Reid heavily involved.
The Republic of Ireland international, playing up front rather than in midfield, showed why three Premiership clubs are after him on his return from a calf injury.
His curling free-kick in the first half was helped onto the bar by Brighton goalkeeper Michels Kuipers.
The match fizzled out after the opening 45 minutes, although Marlon King forced Kuipers into another save with 20 minutes left.
Kuipers suffered a shoulder injury in the closing stages, punching clear a cross from Reid as Kris Commons challenged him.
He had to be replaced by youngster Chris May as Brighton held out to stretch their unbeaten run in the Championship to six games.