Goals from Harvey Barnes and Ademola Lookman were twice pegged back by Adam Webster and Enock Mwepu at King Power Stadium, but City's 100 per cent record in the shootout, plus Neal Maupay's miss and Danny Ward's save from Mwepu, sent the hosts through to the last eight.
Ahead of the draw, here's everything you need to know...
When does the draw take place?
The quarter-finals draw will be conducted at approximately 10:30am on Saturday morning.
You can find out who the Foxes will face on @LCFC social media and LCFC.com shortly afterwards.
Who's still in the competition?
The remaining teams and their ball numbers are listed below...
1. Arsenal
2. Brentford
3. Chelsea
4. Leicester City
5. Liverpool
6. Sunderland
7. Tottenham Hotspur
8. West Ham United
When will the ties take place?
Quarter-final matches will be contested over the week commencing 20 December, 2021.