Kepa Arrizabalaga was the Chelsea hero as he made a string of late saves to deny Saints a place in the last eight as the game at Stamford Bridge ended 1-1 after 90 minutes.
Both goals came minutes either side of half-time as Kai Havertz headed Chelsea into the lead before Southampton hit back quickly when Che Adams bundled the ball home after Kepa parried Kyle Walker-Peters' shot.
The Spain goalkeeper saved from Will Smallbone, Mohammed Salisu and Lyanco to take the tie to a shootout.
Kepa then denied Theo Walcott from the spot and Smallbone blasted over as Chelsea progressed despite Mason Mount's penalty being saved by Fraser Forster.
