Neil Lennon's side sprang out the traps and goals from attacker Mohamed Elyounoussi and Callum McGregor had the Hoops two goals ahead after 21 minutes.
Hibs did what they could to hang on under relentless pressure - and indeed pulled a goal back in the 36th minute through Swedish striker Melker Hallberg.
However, Elyounoussi grabbed his second in the 43rd minute and after the break skipper Scott Brown, who passed a late fitness test, was gifted his first goal of the season.
Hibs half-time substitute Florian Kamberi reduced the deficit with a header immediately but Celtic reasserted and Brown doubled his tally in the final minute of normal time to clinch their 30th successive win in domestic cup ties.
The holders will face either Rangers and Hearts in the final but, regardless of who wins in the other semi-final at the national stadium on Sunday, it will take a mighty effort to dislodge the trophy from Parkhead.
The day started well for the champions with Brown being declared fit following a thigh injury while right-back Jeremie Frimpong, left-back Boli Bolingoli and midfielder Tom Rogic came back into Lennon's side.
For the Leith side, Adam Jackson replaced Ryan Porteous at centre-back and midfielder Josh Vela came in for Glenn Middleton and like the other Hibees players they came in for a battering.
Hibs survived a penalty claim when Elyounoussi's corner appeared to come off the arm of skipper Paul Hanlon but seconds later, in the 17th minute, the Parkhead side were ahead when the Norway international, on loan from Southampton, had the easiest of tasks in heading in a James Forrest cross from six yards out.
Four minutes later, French striker Odsonne Edouard raced on to a long ball from defender Kris Ajer and squared for McGregor to finish from close range.
Paul Heckingbottom's team were under siege but, against the run of play, a Bolingoli tackle outside the penalty area saw the ball break to Hallberg to slide the ball past keeper Fraser Forster from 10 yards for an unlikely lifeline.
That was taken away two minutes from the interval when Edouard unselfishly set up Elyounoussi to knock in from a yard out.
Jonny Hayes replaced Bolingoli for the start of the second half with Kamberi on for Josh Vela and the Celtic attacks continued in waves.
In the 50th minute Elyounoussi fired an angle drive against the post from 14 yards before Forrest's right-footed deflected drive also rebounded off woodwork.
The next goal was a matter of time.
Brown gleefully pounced when Hibs keeper Chris Maxwell fumbled an Elyounoussi corner under pressure from Celtic defender Christopher Jullien to knock in from two yards but the Parkhead fans were still celebrating when Kamberi glanced in a header from a searching cross from Tom James, again giving hope to Hibs.
Celtic survived a spell of pressure and in the final minute Brown raced forward and took a return pass from Elyounoussi to fire past Maxwell after he had parried the first effort, adding more sheen to an impressive performance.