James Milner and Ki-Jana Hoever scored either side of the break to secure victory for a much-changed Reds team and set up a clash with Arsenal in the next phase of the competition.
Here are five talking points from Stadium MK...
A glimpse of the future
Forward Harvey Elliott became the youngest player ever to start a competitive match for Liverpool as manager Jürgen Klopp handed debuts to five youngsters over the course of the 90 minutes.
16 - At 16 years and 174 days old, Harvey Elliott is the youngest ever player to start a competitive match for @LFC… https://t.