Match ends, Brighton and Hove Albion 2, Yeovil Town 0.
Goals from Kazenga LuaLua and Jesse Lingard lifted Brighton into the Championship play-off places and relegated Yeovil into League One.
LuaLua scored in the 77th minute when his left-wing cross eluded keeper Marek Stech and bounced into the net.
Lingard made sure of victory in the second minute of added time, sweeping home Solly March's cutback from the right side of the penalty area.
Brighton move into sixth place until Reading play Doncaster on Saturday.
Albion had the better of the first half, although Yeovil came closest to opening the scoring when Ruben Palazuelos smashed a shot against the crossbar from 20 yards out in the 18th minute.
Andrea Orlandi had the best chance at the other end when his glancing header from Will Buckley's cross went wide of the right post on the half hour.
But almost immediately Brighton keeper Tomasz Kuszczak was forced to save down low to his left from a fierce angled drive from Sam Hoskins.
Joe Edwards had the best chance of the second half for Yeovil when his shot from the edge of the box grazed the top of the bar.
But, with 13 minutes left, the deadlock was broken when LuaLua crossed right-footed from the left and watched the ball bounce in front of keeper Stech, into the back of the net.
It was his first goal since the final day of last season when he scored twice to send Wolves down.
As the game moved into added time Brighton increased their advantage when on-loan Manchester United striker Lingard moved into the centre of the penalty area to connect sweetly with March's cross, his third league goal for the club.
Yeovil Town manager Gary Johnson told BBC Somerset: "Sometimes people don't realise how much it means [to the fans].
"When you look in their eyes you can see how passionate they are and how supportive they've been.
"The reception we got from the Brighton fans as well was fantastic. They knew we'd given it a right go.
"I had a lump in my throat going to our fans and a lump in my throat going to their fans, when they were clapping us off the pitch."
- 4AndrewsBooked at 64mins
- 6StephensSubstituted forForster-Caskeyat 76'minutes
- 11OrlandiSubstituted forMarchat 64'minutes
- 30BuckleySubstituted forLua Luaat 74'minutes
- 9Rodríguez Sánchez
- 25Lua Lua
- 8PalazuelosSubstituted forLanzoniat 86'minutes
- 15DuffyBooked at 54mins
- 9HayterSubstituted forDawsonat 87'minutes
- 11LawrenceSubstituted forDavisat 60'minutesBooked at 73mins
- Andy Madley
- Shots on Target
Second Half ends, Brighton and Hove Albion 2, Yeovil Town 0.
Goal! Brighton and Hove Albion 2, Yeovil Town 0. Jesse Lingard (Brighton and Hove Albion) right footed shot from the centre of the box to the top left corner. Assisted by Solly March.
Leonardo Ulloa (Brighton and Hove Albion) wins a free kick in the attacking half.
Foul by Sam Hoskins (Yeovil Town).
Foul by Kazenga Lua Lua (Brighton and Hove Albion).
Luke Ayling (Yeovil Town) wins a free kick in the attacking half.
Attempt missed. Joe Edwards (Yeovil Town) right footed shot from outside the box is high and wide to the right.
Offside, Brighton and Hove Albion. Lewis Dunk tries a through ball, but Solly March is caught offside.
Solly March (Brighton and Hove Albion) wins a free kick on the right wing.
Foul by Jamie McAllister (Yeovil Town).
Substitution, Yeovil Town. Kevin Dawson replaces James Hayter.
Substitution, Yeovil Town. Matteo Lanzoni replaces Ruben Palazuelos.
Attempt blocked. Solly March (Brighton and Hove Albion) left footed shot from the right side of the box is blocked. Assisted by Gordon Greer.
Foul by Jake Forster-Caskey (Brighton and Hove Albion).
Liam Davis (Yeovil Town) wins a free kick in the attacking half.
Jake Forster-Caskey (Brighton and Hove Albion) wins a free kick in the defensive half.
Foul by Joe Edwards (Yeovil Town).
Goal! Brighton and Hove Albion 1, Yeovil Town 0. Kazenga Lua Lua (Brighton and Hove Albion) right footed shot from long range on the left to the bottom right corner. Assisted by Stephen Ward.
Attempt missed. Kazenga Lua Lua (Brighton and Hove Albion) left footed shot from the left side of the box misses to the left. Assisted by Jesse Lingard.