The Seagulls trailed 2-0 with just 15 minutes to go but levelled with goals from Solly March and Shane Duffy, before Brentford went back ahead four minutes into injury-time.
However, Tomer Hemed rescued a point which Albion deserved for their second half showing as he headed home from six yards with just seconds to play.
Albion made three changes from the 3-1 defeat at Huddersfield on Thursday as Uwe Huenemeier, Steve Sidwell and Jiri Skalak came in for Lewis Dunk, who was serving a one-game ban for his red card at the Terriers, Beram Kayal and Tomer Hemed.
Dale Stephens, Sam Baldock and Gaetan Bong again missed out for the Seagulls, who are also now without Connor Goldson for the rest of the season after it was announced he has been identified as having a heart issue and will have preventative surgery.
Albion midfielder Steve Sidwell glanced a header over from Glenn Murray's cross on six minutes, before the hosts scored twice in six minutes.
Jota finished off a nice passing move by turning home Josh McEachran's cross from close range on 15 minutes.
Jota's free kick went inches over after a slight deflection six minutes later but the hosts doubled their lead from the resulting corner as Dean was left unmarked at the back post to head home.
Jamie Murphy headed a Jiri Skalak free kick well wide as the Seagulls looked for a response. They had a lot more of the ball leading up to half-time and should have got a goal back on 37 minutes as Murphy broke through after hesitation in the Bees defence but dragged his shot wide of the far post from 18 yards.
Anthony Knockaert then stung the palms of home keeper Daniel Bentley in the last action of the half as the Bees led 2-0 at half-time.
Albion introduced Solly March for Jiri Skalak at the break and had a loud penalty shout waved away by referee Jeremy Simpson when Knockaert's shot was blocked early in the second half, before Murray blasted horribly wide after cutting in from the left as the Seagulls made a bright start to the second period.
Brentford had a golden chance to seal all three points when they were awarded a penalty on 57 minutes. Huenemeier tripped Jota but Vibe's spot-kick was kept out by the legs of Stockdale - his third penalty save of the year.
Stockdale then pushed over a powerful Nico Yennaris drive, before Albion introduced Chuba Akpom and Tomer Hemed as they looked for a way back into the game.
Two goals in the space of three minutes then drew Albion level. With 15 minutes to go March crashed an unstoppable strike into the top corner from 20 yards and Shane Duffy then headed the equaliser from Knockaert's cross moments later.
Brighton almost went ahead on 80 minutes when March's shot deflected into the path of Duffy, who was denied by Bentley from ten yards.
Bentley then pushed over a sliced clearance by Dean on 84 minutes, before Hemed headed March's cross over from just a couple of yards in the final minute.
With Albion creating the better chances, it was Brentford who went back ahead four minutes into injury-time when substitute Konstantin Kerschbaumer fired home from 20 yards.
However, there was still time for Hemed to head home Knockaert's cross with just seconds to play as it finished 3-3.
BRENTFORD: Bentley; Bjelland, Dean, Jozefzoon (Canos 69), Yennaris (McCormack 81), McEachran, Woods, Clarke, Vibe, Jota, Field (Kerschbaumer 88). Subs: Bonham, Hofmann, McCormack, Egan, Sawyers.
BRIGHTON: Stockdale; Bruno, Duffy, Huenemeier, Pocognoli; Knockaert, Sidwell, Norwood, Skalak (March 45); Murphy (Akpom 64); Murray (Hemed 70). Subs: Walton, Kayal, Tomori, Towell.
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