It was an intriguing first 30 minutes at the Etihad with both sides jostling for control, but it was the visitors who struck first as Malick Yalcouyé turned in from close-range.
10 minutes later, we struck back as Phil Foden set up Mateo Kovačić to superbly curl into the net from long-range, with the ball kissing the inside of the post on the way in.
Two minutes after the interval, the Seagulls went ahead for the second time of the evening thanks to a neat finish from Georginio Rutter.
With just under 20 minutes left to play, Vitor Reis instinctively flicked in from Rayan Cherki’s drilled free-kick to claim his first goal for the Club.
And with neither side finding a winner in a pulsating 90 minutes of normal time, the tie went to penalties.
After Foden, Pascal Groß, Enzo Fernández, Matt O’Riley, Jeremy Doku and Maxim De Cuyper all scored from the spot, Kovačić was the first to miss seeing his effort saved.
But Rulli saved instantly from Yasin Ayari, before Rayan Cherki scored.
Then Rulli worked his magic again, denying Lewis Dunk to secure our place in the quarter-finals.
View the best images from the thrilling victory via our gallery below.