Stand-in goalkeeper Adrian was the hero as it was his save from Tammy Abraham allowed Liverpool to beat Chelsea 5-4 on penalties.
The Desert Foxes laid claim to the title in a gripping match after a 29-year dry spell.
Tunisia and South Africa filled the final two places for the round of 16 after a tense finish to the group stage in Egypt.
After the last-16 first leg ended goalless at Anfield, five-times European champions Liverpool took control in Munich, bossing the game to become the fourth English team into the last eight
The 26-year-old Liverpool star beat fellow nominees, Liverpool teammate Sadio Mane and Arsenal forward Pierre-Emerick Aubameyang to win African football's 2018 Player of the Year.
Egypt striker Mohamed Salah claimed the honour last year and will be favourite again, hoping to become the fourth player to win back-to-back titles.
It was the first time in World Cup history that a team had been eliminated by the amount of yellow cards they had accrued in the tournament.
Liverpool were 5-0 up, but two late goals by the visiting Italians have given them a glimmer of hope to stage another escape act when the return leg of the Champions League is played in the Italian capital.
Mohamed Salah, Alex Oxlade-Chamberlain and Sadio Mane score three first-half goals for Liverpool to sink Manchester City in the first leg of their Champions League quarter-final play-off at Anfield.
The three shortlisted candidates for the title are: Pierre-Emerick Aubameyang of Borussia Dortmund and Gabon, Liverpool’s Senegalese Sadio Mane and Egyptian Mohamed Salah.
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