But the visitors went for the jugular as Neal saved well from March before Orlandi had a goalbound shot charged down.
Jake Caskey's fierce drive then forced an even better stop from Neal with Vale working hard just to stay in the tie.
Kemy Agustien was next to go close for Brighton when his 64th minute shot crashed against the overworked Vale goalkeeper's right-hand post. Adams brought on strikers Ben Williamson and Jordan Hugill to chase the game, but the visitors countered with a deserved third goal 12 minutes from time.
Ince's first time ball sent Jon Obika sprinting clear of the Vale defence and the on-loan striker from Tottenham rounded Neal and rolled a left foot shot into an empty net from 12 yards.
Promotion-chasing Brighton, with Tuesday's trip to Burnley in mind, made seven changes to the team beaten at Derby last weekend.
And the surface water caused by a pre-match thunderstorm will also have been to Vale's liking with the sodden pitch another leveller.
Much of the early play was bogged down in midfield and a couple of long range efforts by Brighton's Jon Obika and Rohan Ince proved harmless.
Andrea Orlandi went closer when his shot on the turn veered just wide of Chris Neal's right-hand post with the visitors gradually turning the screw.
Neal then had to get down smartly to keep out Solomon March's powerful shot before Brighton broke the deadlock in the 27th minute.
Orlandi delivered an outswinging corner from the left and Ince cushioned a classy left-foot finish high inside Neal's left-hand post from 12 yards
The visitors were on terms within 60 seconds of the restart, midfielder Lansbury rising to level with a superb header from 8 yards following a corner from Majewski.
Keeper Darlow prevented** **Brighton from regaining the lead only 3 minutes later by pushing a goal-bound shot from Barnes onto the post.
Two goals in the space of two minutes put Forest firmly in charge with a strike from Henderson and a spot kick by Lansbury boosting the visitors.
Forest were reduced to 10 men on 67 minutes when Chalobah, booked earlier for a foul, received a second yellow for a push on LuaLua.
LuaLua had a curling free kick saved by Darlow as the Seagulls struggled to launch a late fightback.
LuaLua forced keeper Karl Darlow to make a scrambling save in only the third minute after being fed by Stephen Ward, and two minutes later he fired an angled shot over the bar from inside the area.
Darlow later dived to hold a bouncing 30 yard drive from Ashley Barnes before Forest came close to breaking the deadlock.
An accurate cross from Andy Reid found striker Henderson and his goal-bound header was pushed round the post by Polish goalkeeper Tomasz Kuszczak diving to this left.
Kuszczak was alert again mid-way through the first half when he beat away a firm drive from fellow countryman Radoslaw Majewski.
Lansbury and Reid both put shots wide for Forest before Wales international Crofts put Brighton ahead in the 31st minute from close in.
Lansbury levelled the scores just after half-time, with Forest going in at the interval trailing to Andrew Crofts' header just after the half hour mark.
Two goals in three minutes put Forest in the driving seat, with Lansbury slotting home from the spot almost immediately after Darius Henderson had given them the lead before Nathaniel Chalobah was sent off in the 67th minute as Forest finished the match with 10 men.
Brighton went into the game having scored only four goals in their previous five matches and, in a lively start, former Newcastle winger Kazenga LuaLua provided an immediate threat for the Seagulls.
McGoldrick scored twice inside four first-half minutes - his fourth and fifth of the season - to give Ipswich a 2-0 win and lift them into the Sky Bet Championship's top 10.
Brighton had no answer after McGoldrick's quick-fire brace and seeing a golden chance wasted by midfielder Andrew Crofts with the scores goalless.
Garcia, who was left fuming after referee Stephen Martin waved away second-half appeals for a penalty when Will Buckley's shot hit Tommy Smith's arm, believed McGoldrick was the big difference at Portman Road.
We knew McGoldrick could be a threat and today he showed that he is a player who can play at a higher level. He was the difference between the two sides.
Wanderers had taken a first-half lead after Seagulls winger David Lopez put through his own net, but four second-half minutes saw Brighton score three times to leave Dougie Freedman's men still without a win this season.
Jay Spearing put through his own goal in the 53rd minute, before Inigo Calderon and Will Buckley both found the net to stretch the Amex club's unbeaten run to six matches.
David Ngog failed to keep his cool when one-on-one with keeper Tomasz Kuszczak, who made a save down low to deny the French striker after a mix-up in the Brighton defence.
Millwall were reduced to ten men 14 minutes from time when Dunne received his second yellow card for bringing down Orlandi.
Orlandi had a superb shot from the edge of the box tipped over by Forde before Ulloa rescued a point for Brighton at the far post from a cross by LuaLua.
See all of today's match reports on the ITV Sport football site here
Millwall did a good job of stifling Brighton in the first half and Shittu was there to clear a dangerous low cross by Will Buckley shortly before the break.
The Lions had David Forde back in goal and the Irishman was not tested in the opening period.
Millwall broke the deadlock after 51 minutes through Woolford who calmly slotted home from close in after being set up by Richard Chaplow.
Brighton boss Oscar Garcia, having introduced Andrea Orlandi for Agustien at the break, threw on Kazenga LuaLua in place of David Lopez, and the winger twice had shots deflected wide.