The first half ended goalless despite plenty of class being on show at the American Express Community Stadium.
It was much the same after the break, and it looked as if the game was heading for a 0-0 draw, but Maisie Symonds scored in extra time to snatch a win for Brighton.
After a quiet opening 15 minutes, Kirstie Levell produced a fine stop to prevent a deflected Carter shot from finding the back of the net.
The Foxes then had their best chance of the opening stages when Molly Pike's pass found Esmee De Graaf, but the Brighton keeper beat her effort away.
With ten minutes remaining of the half, both sides were still fighting for scraps.
But the Seagulls took control of the game in the closing stages of the first half, and the Foxes barely got a touch of the ball before the referee called for the break.
The second half got underway, and it continued to be a tight affair despite the Seagulls getting the lion's share of the possession and chances.
Megan Connolly went close from a free-kick that failed to dip in time to find the back of the net.
And the hosts threatened from Connolly's in-swinging corner, but Levell was able to hold on to Victoria Williams' header and keep the scores level.
But then there was a dramatic scramble in the Seagulls box, which saw the ball find the back of the net, however, it was after the referee had blown his whistle and the game remained deadlocked.
But it was ecstasy for Brighton when substitute Symonds scored the winner from a superb free-kick during added time to keep the three points in the South Coast.
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Brighton (5-3-2): Megan Walsh; Emma Koivisto, Maya Le Tissier, Danique Kerkdijk, Victoria Williams, Felicity Gibbons; Ellie Brazil, Megan Connolly, Aileen Whelan; Guem-min Lee, Danielle Carter
Substitutes: Inessa Kaagman for Ellie Brazil 54', Maisie Symonds for Danielle Carter 75', Katie Robinson for Megan Connolly 86', Emily Simpkins for Felicity Gibbons 86'
Substitutes not used: Frances Angel, Libby Bance, Kayleigh Green, Katie Robinson,
Goals: Maisie Symonds 90+3’
Leicester City (3-4-3): Kirstie Levell, Georgia Brougham, Abbie McManus, Ashleigh Plumptre, Jemma Purfield, Shannon O'Brien, Sam Tierney, Sophie Howard, Molly Pike, Esmee de Graaf, Jess Sigsworth,
Substitutes: Paige Bailey-Gayle for Shannon O'Brien 69', Natasha Flint for Jess Sigsworth 75'
Bookings: Paige Bailey-Gayle 75'
Ref: Ryan Atkin