Birmingham opened the scoring inside five minutes with a powerful close-range effort by Sarah Mayling after Abbi Grant’s cross from the left, before Brighton drew level in the 25th minute courtesy of captain Danielle Bowman’s calm spot-kick.
Mollie Green restored Birmingham’s lead with an early second-half penalty but Brighton upped the intensity and were rewarded for their efforts with a last-minute equaliser.
Substitute Denise O’Sullivan, on loan from North Carolina Courage, found herself unmarked in the box and headed home Fliss Gibbons’ cross to take the match to extra time.
A flurry of opportunities followed. Rianna Jarrett’s strike was well stopped by Birmingham goalkeeper Hampton, while Jamie-Lee Napier went close with a curling shot at the other end, but the two sides could not be separated and it remained 2-2.
Brighton’s Kayleigh Green and Birmingham’s Claudia Walker both missed but Hampton saved from Megan Connolly before Georgia Brougham scored the winning penalty.
Albion head coach Hope Powell said, "I honestly think we were the better team, certainly when we brought some fresh legs on.
"In the first half we weren’t very good but credit to them. We knew it would be a different proposition to when we last played them. We took too long to get going and by that time you are chasing the game and it starts to sap your energy.
"I think we did really well to come back from a goal down twice, we were just unlucky with the penalties."
"Credit must go to Birmingham," said Powell. "They were very resilient and made it very difficult when they sat back, and they were hard to break down.
"We made some changes, brought on some fresh legs and I think itt shows that we can now bring players on and add a little bit of something else. The strength in depth in the squad is really good.
"But at the end of the day they won albeit not in the 120 minutes and we have to move forward. It would have been nice to progress to a semi-final but we still have this season's FA Cup to look forward to and the WSL is obviously our priority."
Birmingham will now face Everton in the semi-finals on September 30.