French striker Moussa Dembele scored a double after coming on as a substitute at Hampden

Holders Celtic held off a second-half fightback from Hibernian at Hampden to reach the Scottish League Cup final.

Mikael Lustig twice took advantage of poor defending at the far post to sweep Celtic into a 2-0 lead at half-time.

Anthony Stokes pulled one back from the penalty spot, but Celtic substitute Moussa Dembele beat the offside trap to restore the two-goal lead.

Oliver Shaw finished off a sweeping move to make it 3-2, but Dembele raced clear late on to seal a final spot.

Celtic will meet Rangers or Motherwell in the final, with the two meeting in the other semi-final on Sunday.

Mikael Lustig turned home the opening goal for Celtic after sloppy defending from Hibernian

Hibs got off to the kind of start that Neil Lennon would have imagined only in his nightmares. The confusion in his defence for Lustig's opener was a catastrophe, Stuart Armstrong dinking in a cross from the left which Dedryck Boyata flicked onwards to the back post.

Brandon Barker went to sleep in the moment, allowing Lustig in to put his shot past Ross Laidlaw in the Hibs goal. The bitter irony for Lennon was that his defence looked at ease before that goal and then again directly after. They did precious little in attack, Stokes being far too isolated up front, but nor were they being peppered with shots at the other end.

Celtic weren't close to their best, but even as an underpowered force they went two goals clear when another calamity befell Hibs at the back. This time it was a corner that did the damage. Leigh Griffiths put it in, David Gray lost Lustig and when his tame volley came at Laidlaw, the Hibs goalkeeper made a desperate hash of making what should have been a routine save.

Defender Lustig was over the moon after netting his second of the day

Lennon made two changes at the break, Martin Boyle appearing for Marvin Bartley and Steven Whittaker coming on for Gray. Immediately, Hibs were better. Where before they posed no threat, now they were giving Celtic something to think about.

Vykintas Slivka should have scored after a terrific pass from Whittaker, but put it wide. That, though, was just the beginning for them. Just short of the hour they pulled a goal back from a penalty that should never have been given.

It was Celtic's turn to get messy at the back, Boyata getting ransacked in possession, a dispossession that sent Hibs on their way. Boyata thought he had redeemed himself when poking the ball away from the falling Boyle in the box. After consultation, referee Kevin Clancy pointed to the penalty spot.

There was a tumult among the Celtic support, but Stokes took no notice. He sent Craig Gordon the wrong way and put his team back in the semi-final.

Anthony Stokes gave Hibs hope from the penalty spot

The penalty was down the Hibs end, in front of thousands of empty seats, tickets that the club asked for but could not sell. The deserted section was an eyesore, an embarrassment for Hibs and for the SPFL. Celtic would have easily filled that area had they been afforded the opportunity.

Where before it was Lennon making a double substitution, now it was Brendan Rodgers' turn. On came James Forrest for the ineffective Patrick Roberts and in came Dembele for Griffiths. The Frenchman was on the field for just five minutes before he scored.

Again, it was a goal that would have had Lennon in a rage. Armstrong drove the ball into the box from the left, Forrest picked up on the far side and banged it in from the right to Scott Sinclair who scuffed a shot into Dembele's path. All alone a few yards out, Dembele scored comfortably.

Oliver Shaw scored his first goal for Hibs to make it 3-2

That looked to be that, but Hibs came again. Whittaker picked up outside the box and slid a gorgeous pass in behind Nir Bitton, playing centre-half, to substitute Shaw. The 19-year-old's run was outstanding and his finish was just as good. Game on again.

Hibs pressed hard for the equaliser but that, of course, left them short at the back and Celtic fed off that. Laidlaw had to save from Forrest, then he made a fine block from Dembele. He was caught in the end, though. And it was Dembele who caught him.

More slack play in their own half opened the door to Celtic. When they came steaming downfield, Dembele curled a precise shot around the advancing Laidlaw for the fourth.

For Hibs, regret and pain. For Rodgers and Celtic a 60th consecutive game unbeaten in domestic football, another cup final and, perhaps most significantly, the return of an old metronome in Dembele.

The striker hadn't got going this season before this. It's safe to say, he has now.

Dembele sealed Celtic's win with a double after coming on as a sub