On-loan striker Sam Vokes' goal at the City Ground appeared to have been enough to ensure the Seagulls completed an east midlands double following victory over Derby in the Championship on Tuesday.
But substitute Matthew Sparrow was sent off for the visitors in the closing stages and the hosts took full advantage when Lynch pounced to poke in from close range.
It was the least Forest deserved after they struck the woodwork three times and created the bulk of the chances.
Andy Reid's curling free kick crashed off a post but the Seagulls woke up just after the hour mark when Vokes timed his run to perfection to head Vicente's free-kick into the net.
Adlene Guedioura and Dexter Blackstock saw efforts come back off a post but, minutes after Sparrow was dismissed for two cautions, Lynch popped up with the leveller.
Guedioura scored Forest's first in a 7-3 victory at Leeds in midweek with a piledriver from distance and the home crowd encouraged him to replicate that in the 21st minute but he flashed his effort wide from distance.
Lewis Dunk cynically fouled Guy Moussi on the edge of the box and Reid bent the resulting free kick around the Brighton wall but his effort crashed off a post.
That galvanised the lacklustre Forest and Reid's hanging delivery was nodded just wide by Blackstock.
Guedioura's personal mission to eclipse his stunning strike on Tuesday continued as he chested the ball down before fizzing a fantastic volley narrowly wide.
The visiting side had struggled to fashion any chances but in Vicente they possessed the one player capable of creating an opportunity, and the Spaniard's free-kick led to the opening goal in the 62nd minute.
Vokes broke the Forest offside trap and met Vicente's enticing set piece with his head to score with Brighton's first effort on target.
Forest refused to let their heads drop and Blackstock teed up Guedioura whose fierce shot was punched away by keeper Peter Brezovan.
Guedioura continued to hammer in efforts from distance and he slammed a 25-yard chance against the post.
The impressive Vicente was withdrawn as Poyet looked to consolidate his side's one-goal advantage.
Substitute Ishmael Miller created havoc from a Reid corner and Blackstock's tame effort rolled against a post before the ball was cleared.
Sparrow, a second-half replacement, was dismissed in the closing stages for a second yellow card after he pulled back Guedioura and Forest still had time to make use of their numerical advantage.
A long ball into the Brighton box was flicked on by Blackstock and, after Brezovan had flapped at the ball, Lynch lashed in a dramatic equaliser.