Jurgen Klopp made wholesale changes, with none of the starting 11 from Sunday’s Premier League match at Chelsea even in the squad, debuts were handed to goalkeeper Caoimhin Kelleher, winger Harvey Elliott and striker Rhian Brewster.
Elliott was Liverpool’s most lively player throughout, with one beautiful first-half cross leading to James Milner heading wide.
It was Milner who opened the scoring shortly before half-time after his stinging half-volley was fumbled over the line by MK Dons goalkeeper Stuart Moore.
Naby Keita played for two-thirds of the game, and although he failed to catch the eye, it was an invaluable run-out for the Guinean on his return from injury.
Alex Oxlade-Chamberlain, like Keita, was a little subdued, but one superb effort flew off the post in the second half.
Hoever doubled the lead with a well-taken header, becoming the fourth-youngest goalscorer in Liverpool’s history – behind Ben Woodburn, Michael Owen and Jordan Rossiter.
Klopp applauded the travelling away supporters after the final whistle, with the fourth round draw pitching the Reds at home to Arsenal in late October.
Next up is a trip to Sheffield United in the Premier League on Saturday lunchtime, as Liverpool look to retain their 100 percent start to the season.