The visitors broke the deadlock early in the first half before finding two goals in the last 20 minutes to seal the victory.
It was a frantic start to the match, with both sides looking to grab an early goal.
The wee Hibees were pressing from the front and forcing Celtic to make some snap decisions, in the hope of picking up a turnover and making the visitors pay.
And the game plan nearly paid off; after an intense start, Josh Landers had the first opportunity of the match in the 11th minute.
A long ball from the back looked to be too much for Landers to deal with, but the young striker's grit and determination allowed him a free run in at goal. Landers looked destined to open the scoring, but his final touch was too heavy, allowing the Celtic keeper’ to smother the ball at close proximity.
Three minutes later, it was Celtic who found themselves ahead.
Some decent passing down the left-hand side allowed their winger to whip in a teasing cross. The Hibs backline was unable to deal with it, leaving a simple tap-in for their no.7 at the back post.
Hibs didn’t let the goal dishearten them and kept their shape well as Celtic looked to double their lead.
Freddie Owens was kept busy in goal and was grateful for his woodwork on several occasions as the away side grew in confidence.
Chances were few and far between for Hibs throughout the remainder of the first half, but they could have brought themselves level from a corner in the 37th minute. Reuben McCallister delivered an excellent set piece and Owen Hastie rose well, but he could not direct his header goalwards.
The Hibees picked up the tempo heading into the second 45 and had two glorious opportunities to draw their side level.
Reece Holden was finding gaps down the left wing and managed to pull a ball back to Josh Landers, who was hovering around the edge of the box. Landers connected well but was unable to keep his strike down.
Moments later, Adam Khan was bullish in the middle of the park, winning the ball back and setting up Rudi Molotnikov, but the midfielder dragged his effort wide of the target.
The wee Hibees were slowly clawing their way back into the tie but an unfortunate lapse in concentration allowed Celtic to double their lead from a corner in the 71st minute.
Celtic dominated the ball following their second goal and added another 10 minutes from time. A driving run down the right-hand side from Celtic’s no.7 opened up gaps in the defence. His effort was saved well by Owens, but Celtics striker reacted quickest and sealed the game with the third goal.
A valiant effort from the Hibees but unfortunately not enough to take anything out of the game.
F. Owens, N. Geaney, R. Waugh, A. Khan, O. Hastie, J. MacIntyre, B. Mckenzie, R. McCallister, J. Landers, R. Molotnikov, R. Holden
