In what was an entertaining cup tie, Callum Robinson put the Baggies ahead early in the second-half.
But Albion's hopes of reaching the fourth round were dealt a huge blow when Cedric Kipre received his marching orders following two yellow cards in the space of just a few minutes.
And up against 10 men, Premier League Brighton took control with Neal Maupay winning the game for them with a strike in the first half of added-on time.
Albion headed into the game with Sam Johnstone and Alex Mowatt suspended following the red cards they picked up against Cardiff.
Loanees Matt Clarke and Jayson Molumby also couldn't play against their parent club while Daryl Dike wasn't considered to allow him to work on his fitness.
But at his pre-match press conference, Ismael said he would name the strongest team he possibly could against the Seagulls.
And so it proved with David Button getting the nod in the goal and Kipre, Kyle Bartley and Conor Townsend the back three.
In Ismael's 3-4-3 formation, Darnell Furlong operated at right wing-back with Adam Reach on the left and Jake Livermore and Taylor Gardner-Hickman the midfield two.
Up front, Matt Phillips returned from a muscle problem to start as the central striker with Robinson and Karlan Grant either side.
Brighton also named a strong side with Joel Veltman, Dan Burn, Enock Mwepu and Maupay retaining their place following the 3-2 win at Everton.
They lined up in a 3-5-2 system with Danny Welbeck joining Maupay in attack.
It was Albion, with Phillips in particular looking bright, who started the better of the two teams with Ismael's side some producing some nice passages of play in the opening 20 minutes.
But it was Brighton who created the first clear-cut chance when a fabulous pass from Pascal Gross put Welbeck in on goal.
The former England international then charged into the box only for Button to keep out his strike with a smart block.
Albion's best chance arrived in the 37th minute when Phillips found Livermore in the box.
He then hit a fierce strike that deflected off Shane Duffy before flying wide.
The cup clash continued to be open and keenly contested from that point.
But Brighton really should have got themselves ahead just before the break when Kipre and Bartley needlessly got in each others way.
That allowed Maupay to be played in on goal. But just like Welbeck earlier, he was denied thanks to an excellent block from Button.
That miss proved costly when Albion opened the scoring just minutes after the re-start.
A bursting run from Grant saw him leave Burn for Dust.
And he then sent in a low cross which Robinson lifted over Kjell Scherpen and into the net.
The Baggies hopes of holding onto their lead were dealt a blow when Kipre was given his marching orders after picking up two yellow cards in quick succession.
And from the free-kick from the second booking, they should have pulled level with the ball whipped in only for Burn to side-foot over from close range.
In the 81st minute, though, the visitors did pull level when substitute Moder collected the ball in the box before lashing a strike past Button.
Brighton almost won it inside the 90 minutes when Button produced a fantastic low stop to keep out an Alexis MacAllister strike.
The Seagulls won it with a goal in first-half of extra time.
Moder sent in a cross that Trossard cleverly let go through his legs. And Maupay was then on hand to fire in.
And they went on to see out the game comfortably from that point.
Albion (3-4-3): Button, Kipre, Bartley, Townsend, Furlong, Livermore, Gardner-Hickman (Ashworth 68), Reach, Robinson (Taylor 79), Phillips (Diangana 64), Grant (Fellows 79).
Subs not used: Palmer, Castro, Tulloch, Hugill.
Brighton (3-4-3: Scherpen, Veltman (Ferguson 76), Duffy, Offiah (Cucurella 55), Burn, Mwepu (MacAllister 28), Alzate (Moder 76), Gross, March, Maupay, Welbeck (Trossard 55).
Subs not used: Sanchez, Leonard, Turns.