Moussa Dembele, the hero of the last round when his penalty sealed victory over Astana, then headed home in the 73rd minute following an inspired substitution from manager Brendan Rodgers.

Captain Scott Brown made it 5-2 in the 85th minute to ease the pressure for the return leg in Israel next Tuesday, as the Scottish champions hope to clinch a place in the group stages of Europe’s elite competition for the first time in three years.

“It was a brilliant result. You would obviously prefer 3-0 but 5-2 really shows the level that the team played at,” said Rodgers.

“From 3-2 to then go and win the game 5-2 shows the mental strength of the players as well as their quality.”

Hapoel manager Barak Bakhar said it was a crazy match.

“It is hard to analyse a match like that. We started the match very badly but we came back and were close to equalising,” he said. “We showed our qualities and we hope to do the unbelievable next week.”

The home side had an early chance when Kieran Tierney’s cross worked its way to Brown whose shot was turned round the post by David Goresh.

The Hapoel keeper’s good work was undone when he contributed to Celtic’s opener.

Goresh took out Scott Sinclair as he chased down Griffiths’ excellent pass over the top of the defence, but Socceroos midfielder Rogic pounced to blast the loose ball into the net from the edge of the box as referee Damir Skomina allowed a good advantage.

Celtic looked dangerous in every attack and got the second goal their play merited.

Sinclair rolled the ball out wide to James Forrest whose cross from the right found Griffiths at the back post and the striker sent a powerful downward header bouncing beyond the keeper.

There was more to come in stoppage time as Griffiths added his second when the striker earned his side a free-kick on the right of the box.

Griffiths picked himself up and curled home a wonderful left-foot effort that flew into the top corner to beat Goresh at his near post.

The hosts saw some of their good work undone in a two-minute second-half spell. Lucio pulled one back when he found space in the box to fire a low shot that beat Craig Gordon at his near post.

The hosts barely had time to recover before Anthony Nwakaeme showed a good turn of pace to drive into the Celtic box and pull the ball back for Melikson who drilled into the net from 18 yards out.

Dembele replaced Rogic in the 70th minute and three minutes later he got the deftest of touches on a Griffiths corner to guide a header past Goresh.

Brown made a meal of his initial effort from a Forrest lay-off, but made no mistake with the second attempt as he volleyed home.