Celtic set up a meeting with second-tier Falkirk in the Premier Sports Cup quarter-finals by brushing aside Hibernian for the second time in a week.
Daizen Maeda tucked in the opening goal after just three minutes and added a second barely 13 minutes later as the Premiership champions coursed with confidence.
The Japan forward had three further chances to net his hat-trick before the break, such was Celtic's dominance.
However, Mykola Kuharevich's superb diving header from Martin Boyle's free-kick got David Gray's side back in the game and shifted the momentum.
Hibs' improvement continued into the second half, but then a horrible error from Marvin Ekpiteta undid all their good work.
The centre-back's square pass to Josef Bursik was weak, and the Hibs goalkeeper clattered the ball into the onrushing Nicolas Kuhn, who spun away in celebration as the ball trundled into the net.
From there, any serious hopes of a comeback faded. In the absence of Kyogo Furuhashi, who was rested as he continues to manage a shoulder injury, Adam Idah came off the bench to mark his return on a permanent deal from Norwich.
That capped a productive afternoon for Celtic, who will be determined to reclaim the only domestic trophy they failed to win last term.
Their next step is a home tie with second-tier Falkirk, who knocked out Hearts in the last 16, on the weekend of 21 September.
Ominous Celtic overpower struggling Hibs
Celtic have started the season confidently, which is rather ominous for everyone else. In the opening half hour they threatened to blow Hibs off the park.
A combination of ferocious pressing, quick passing, and incisive forward runs had the home fans purring at Celtic Park.
First the improving Kuhn held his width and played in Hatate, who squared for Maeda to score neatly.
Then Kuhn's chipped ball allowed Maeda in behind to prod past Bursik. It was the blueprint for how Brendan Rodgers wants his team to play.
The frustration, though, for the Northern Irishman will be how one lapse allowed Hibs back into the game and there was also some wastefulness in front of goal.
But despite the lack of fresh faces, they look well set to go for another domestic treble. But the lingering question is whether they will strengthen further to make more of a fist of the revamped Champions League.
Hibs, meanwhile, were asked by new head coach Gray to be "miles better" than a week ago at Easter Road.
They lasted only a further 65 seconds without conceding. A switch to a back three made little difference as they were tormented for most of the first half.
However, Kuharevich's header was superb and after it Hibs looked more menacing as they went direct and looked to unsettle Celtic physically.
That was blown up by Ekpiteta's horrible error, which added to a growing list for the defender even at this stage of the season.
It's early days but Hibs don't look like a team with the personnel to play from the back, and it's unclear exactly how Gray envisages his team operating.
However, with nine new faces in and potentially more on the way that could be a slow process for the Hibs boss, who should not be judged so early on back-to-back games against Celtic.
What they said
Celtic manager Brendan Rodgers: "I thought we were excellent from the start of the game. We showed our hunger. We said before the game that our playmaker today would be our counter pressing.
"It was there and we were winning so many second balls. Our only real danger was from throw-ins. They've got guys on either side who can throw it in and add a little bit of pressure and make you fret a little bit.
"We dealt well with that, and their header was a great header. We don't have any complaints. We could maybe have shifted our wall back a bit but we'll learn from that."
Hibernian head coach David Gray: "We found ourselves very quickly in the same movie again, which is extremely frustrating.
"For the first two minutes of the game, we were front-footed but individual errors have cost us again. We've lost a goal after three minutes again.
"There's no excuses for the level of performance and the goals we're losing at the moment. There's going to be competition and there will have to be changes because we can't keep making the same mistakes."
