City stayed on course to retain the title by twice coming from behind to draw 2-2 with Brighton at home on Wednesday (Thursday AEDT), then triumph 4-3 in the shootout.
Backup goalkeeper Gerónimo Rulli saved Brighton's last two spot kicks — from Yasin Ayari and Lewis Dunk — to rescue City, who had fallen behind in the shootout when Mateo Kovacic had the team's fourth penalty saved.
In a match that finished a half-hour later, Liverpool beat Chelsea 6-5 in a shootout after a 1-1 draw in which both goals also come from the penalty spot.
Wesley Fofana missed what proved to be the final kick of the shootout, smashing it well over the crossbar and into The Kop at Anfield as Liverpool fans roared in delight.
Arsenal weren't so lucky in a shootout on Tuesday, losing in stunning fashion to fourth-tier minnow Fleetwood Town in one of the biggest shocks in the competition's 66-year history.
In other all-Premier League last-16 matchups on Thursday AEDT, Bournemouth beat Aston Villa 3-0, Crystal Palace won 1-0 at Fulham, and Sunderland overcame Brentford 3-2.
Third-tier Bradford City, the beaten finalist in 2013, joined Fleetwood in advancing to the last eight on Tuesday.
On Friday AEDT, Everton host Newcastle to wrap up the last 16.
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