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Leigh Griffiths headed Celtic's second of the night

Celtic took a giant step towards the Champions League group stage with an extraordinary play-off first-leg win over Israeli side Hapoel Beer Sheva.

Brendan Rodgers' team were utterly dominant in the opening half, scoring through Tom Rogic and a terrific double from Leigh Griffiths.

The wheels fell off suddenly early in the second half as Lucio Maranhao and Maor Melikson netted.

But Moussa Dembele headed in a fourth and Scott Brown rattled home a fifth.

The two sides meet again in Beersheba on Tuesday but that game will have to go some to match a brilliant and madcap European night at Celtic Park.

Craig Gordon's magnificent save from a Maharan Radi header preserved Celtic's lead at 4-2 and Hapoel had a penalty claim turned down shortly before Brown's goal.

A late goal by Brown (centre) restored Celtic's three-goal advantage

One half, three goals

For Celtic, it had been so easy for so long.

Griffiths was so involved in the first half it was difficult to keep a check on how many versions of himself were out on the pitch. Scott Sinclair's pace troubled Beer Sheva, Rogic had a field day and Brown led the side well.

Celtic were ahead when Griffiths dinked a beautiful ball over the visiting defence to Sinclair, who was promptly taken out by goalkeeper David Goresh. It would have been a penalty had it not been for Rogic following up to drive Celtic into the lead.

Soon after, Sinclair went down in the box but a big shout for a spot-kick was waved away. It hardly seemed to matter because in Celtic's performance there was always the promise of more goals. And they came.

Kolo Toure strode out of defence and found Sinclair, who put James Forrest away down the right. His cross was nutted home brilliantly by Griffiths.

The third was even better, a sumptuous Griffiths free-kick from wide to the right of the Hapoel penalty area. The striker curled into the top corner. Total class.

Second-half scare

Melikson (centre) brought Hapoel back to 3-2

Hapoel had no shots on goal and, seemingly, no hope of turning it around, but they did.

From a counter-attack, Lucio struck from close range to make it 3-1. From another advance down the left two minutes later, Melikson drove home from a central position and suddenly it was 3-2.

Celtic were in shock, but gathered themselves to score a fourth. Griffiths was involved again, swinging in a corner for Dembele to head home.

Gordon's superb save from Radi was as impressive as it was critical.

And then Brown added the dramatic flourish, his first shot fluffed, his second rifled into the Hapoel net to send Celtic Park back into a blissful state.

To call it a classic does not quite cover it.