The hosts had several chances to get on the board against a youthful Liverpool XI but solid second-half goalkeeping by Caoimhin Kelleher ensured the Reds' win in front of a club record 28,521 attendance at Stadium MK.
Liverpool's first came in the 41st minute after MK Dons goakeeper Stuart Moore mishandled Milner's driving strike from outside the penalty box.
Hoever then scored his first senior side goal in the 70th minute on header to the back post off Milner's floating cross.
Liverpool manager Jurgen Klopp praised Milner's performance on the night.
"This man is on fire," said Klopp of his side's captain. "He is a real role model for young players. The team had a lack of experience and a lack of rhythm and the player with the most experience and rhythm was the best player."
K Dons missed two stellar chances through Conor McGrandles and Sam Nombe, while Jordan Bowery hit the post in the second half before Hoever's goal.
"I was proud of the way we played and I'm disappointed we didn't score a goal," MK Dons manager Paul Tisdale said.
Caoimhin, Rhian Brewster, and 16-year-old Harvey Elliott were those who made their Liverpool senior debuts in the win. Elliot, the youngest ever to start in Reds competitive match, nearly scored on two different occasions only to hit the crossbar twice.
"At 16 years old still and he is this kind of footballer. That is really good for us. He is a brilliant boy, he takes the situation really well and wants to learn," Klopp said of Elliott.