Hibs came within inches of forcing extra time when Kevin Nisbet hit the post just two minutes from time with a header. Hanlon couldn’t turn to rebound into the net.
Another chance arrived in stoppage time, but Joe Newell and Ryan Porteous were kept out.
Hibs will feel hard done by. They had a good claim for a penalty turned down late in the second half when Carl Starfelt appeared to shove Ryan Porteous in the box and Celtic’s equaliser had more than a hint of offside about it. Smoke bombs made it difficult to say for sure whether Kygo was onside or not.
Hanlon had headed Hibs in front a minute earlier on 50 minutes, only for Kygo to grab his controversial equaliser seconds later.
The Japanese striker was beyond the Hibs centre backs when he latched on to a long ball over the top to fire under Matt Macey, but there was no doubt about the validity or quality of his second on 72 minutes.
Hibs were on the back foot throughout the first half, with Celtic enjoying 73 per cent possession. But the Hibs back four of Paul McGinn, Ryan Porteous, Hanlon and Lewis Stevenson were comfortable.
For all their domination of the ball, Ange Postecoglou’s side were fairly predicable and didn’t really creating clear-cut chances.
The best of them came early on and was a heart-in-mouth moment for the Hibs fans.
A powerful low drive from Celtic left-back Greg Taylor was spilled by Matt Macey, the goalkeeper recovering to get a hand to Liel Abada's follow-up and centre-half Paul Hanlon came in to hook off the line. But the offside flag had already gone up.
The game sprung into life early in the second half when Hanlon headed Hibs in front from Boyle’s corner, only to concede an equaliser a minute later.
Hanlon’s goal was the first effort on goal Hibs had made, but they certainly made it count.
The centre-half made his run towards the back post and could not be stopped as he powered a downward header towards goal. It crossed the line despite attempts by Josip Juranovic and goalkeeper Joe Hart to keep it out.
The explosion of joy in the Hibs end was short-lived, however.
Within a matter of seconds Kygo Furuhashi raced clear as a ball was played over the top and the ruthless Japanese forward fired his shot under goalkeeper Matt Macey from an acute angle.
There was more than a hint of offside, but there was no flag from the linesman and Celtic were level.
Kevin Nisbet should probably have put Hibs back in the lead as he pounced on a slip from Carl Starfelt before turning the Celtic centre-half inside out. But the Scotland striker was foiled by the legs of outrushing goalkeeper Joe Hart.
It was another ball over the top of the Hibs defence that gave Kyogo his second.
A quickly taken free kick from Tom Rogic picked out the Japan striker and he clipped it over the advancing Macey to seal the deal for Celtic.
Hibs pushed Poreous up front and went the aerial route as they tried to apply late pressure on the Celtic defence.
Nisbet hit the post, Hanlon missed the rebound and a late double chance for Joe Newell and Ryan Porteous was also kept out.
It was the chance Hibs were waiting for but Newell's shot was beaten away by goalkeeper Joe Hart and Porteous' effort on the rebound was blocked.
It just wasn’t meant to be.
Hibernian: Macey; McGinn, Porteous, Hanlon, Stevenson (Doidge 80); Doyle-Hayes, Newell; Boyle, Campbell (Allan 77), Murphy (Doig 80); Nisbet. Subs not used: Dabrowski, Wright, Gogic, McGregor, Scott, Cadden.
Celtic: Hart; Juranovic, Carter-Vickers, Starfelt, Taylor (Ralston 75); McGregor; Abada, Turnbull (Bitton 27), Rogic, Johnston (Scales 83); Kyogo (Moffat 83). Subs: Bain, McCarthy, Shaw, Montgomery, Welsh.
Referee: John Beaton