The Reds have beaten Brighton only once in the last eight meetings between the two sides – and Stuart Pearce’s side rarely looked like adding to that tally on Saturday.
With Norwich winning 3-1 at Blackpool, Forest slipped down into second place in the table, following a game in which they rarely found their attacking threat.
Brighton had not lost in four previous visits to the City Ground and Forest were making hard work of ending that run during a first half in which they failed to make the most of long spells of dominance.
Henri Lansbury powered a header high of the target following a superb cross from wide on the left from Danny Fox, Chris Burke saw a powerful strike, with the outside of his right boot, charged down by the retreating Kazenga LuaLua and Britt Assombalonga fired wide after a defensive mistake laid on a golden chance for the striker.
It was the unlikely figure of Robert Tesche, the free transfer signing from Hamburg, who looked the most likely to put the home side ahead, however.
The German saw a low, driven volley deflected wide of the post and fired another just high and wide of the target.
And Brighton needed a superb save from David Stockdale, diving high to his right, to deny Tesche a third time, after yet another driven shot from the Forest man had taken a wicked deflection, sending it spinning towards the corner of the net.
Brighton had a dangerous spell of their own just before the interval, with Adrian Colunga spurning a decent opening, firing a shot straight at Karl Darlow, after being picked out by LuaLua, just inside the penalty area.
Another rapid counter almost saw the visitors snatch the lead, but Craig Mackail-Smith saw his glancing header drop wide of the post after Bruno Saltor had picked him out with a pin-point cross from the right.
The second half, like the first, began in scrappy fashion.
Mackail-Smith had a shot deflected wide of the post and Lansbury bundled an effort wide but, generally, chances were even fewer in number, with Forest limited to long-range efforts from Antonio and Lansbury.
Lars Veldwijk might have scored with his first touch, after coming off the bench, but bundled the ball into the side netting, after battling to connect with a Fox free-kick.
Mackail-Smith was a foot away from snatching all three points for Brighton as he flashed a shot across the face of goal after angling into the box from the left.
Michael Mancienne should have won it for Forest in stoppage time, but powered a free header, from a Ben Osborn corner, into the turf and over the bar, from eight yards out.