The Japan international started in the absence of compatriot Kyogo Furuhashi, while Adam Idah made his return off the bench after sealing a permanent move from Norwich this week.
Maeda took a rare chance to start as a centre-forward with two cool finishes inside the first 15 minutes.
Mykola Kuharevich pulled a goal back for Hibs before half-time with a spectacular diving header.
But any hope of a fightback from the visitors was quashed when Nicolas Kuhn charged down Hibs goalkeeper Josef Bursik's attempted clearance to restore the Scottish champions' two-goal lead.
"Overall, the speed and tempo in the game and the quality in the attacking moments was fantastic," said Celtic manager Brendan Rodgers.
Celtic will face Championship side Falkirk, who knocked out Hearts on Saturday, at home in the last eight.
Holders Rangers will entertain Dundee.
Aberdeen take on fourth-tier Spartans, while Dundee United and Motherwell face off after they also booked their place in the quarter-finals on Sunday.
