The play-off tie looked dead and buried in the Hoops’ favour at the interval when Leigh Griffiths struck with a header and brilliant free-kick after attacking midfielder Tom Rogic opened the scoring.
However, two goals in two minutes after the break from Brazilian striker Lucio Maranhao and skipper Maor Melikson had the Israeli side back in the game and the Celtic supporters in mild panic.
But substitute Moussa Dembele gave the Scottish champions some breathing space when he made it 4-2 from a Griffiths corner and tireless skipper Scott Brown grabbed a fifth in the 86th minute.
Celtic Park was all but full and in good voice at kick-off, the fans recognising the magnitude of the game although the Palestine flags displayed by a section of the home support could have disciplinary ramifications for the Glasgow club.
In a frenzied start to the game, the goal was not too long in coming. Griffiths set Scott Sinclair free with a defence-splitting pass and when goalkeeper David Goresh clattered the former Aston Villa forward just inside the box Rogic followed up to knock the ball into the net and Celtic Park erupted.
Rogic, brimming with confidence, then had a low drive from outside the box saved by Goresh but Hapoel tried to push forward and indeed looked slick and confident enough to a point but the Glasgow side were relentless.
In the 35th minute, as play swung to and fro, Sinclair failed to connect properly with a Kieran Tierney cut-back allowing Goresh to gather.
However, five minutes from the interval Griffiths was much more clinical when he met a James Forrest cross at the back post to bullet his header into the net.
The former Wolves forward was not finished.
After defender Shir Tzedek clambered on him outside the box to pick up a booking Griffiths picked himself up and sent a textbook curling free-kick into the top corner.
The half-time whistle sounded amid Celtic Park uproar and the home side went for more goals after the break.
However, the complexion of the game changed dramatically in a two-minute spell.
Striker Lucio Maranhao drifted too easily into the Celtic penalty area before beating Gordon with a drive and as the Parkhead side momentarily reeled, skipper Melikson drilled in a shot from the outside of the box.
One by one, on came substitutes Nir Bitton, Saidy Janko and Dembele for Callum McGregor, Mikael Lustig and Rogic respectively as Rodgers looked for reassertion and the latter did exactly that three minutes after coming on when he headed in a Griffiths corner in the 73rd minute.
It was frenetic, breathless entertainment.
As Hapoel responded, Gordon made a great save from Maharan Radi’s close-range header but it was Brown who restored Celtic’s three-goal advantage in the 86th minute with a volley from 12 yards.
Gordon, Lustig (Janko 62), Toure, O’Connell, Tierney, Forrest, Brown, Rogic (Dembele 70), McGregor (Bitton 60), Sinclair, Griffiths.
Goresh, Biton, Hoban (Buzaglo 79), Taha,Tzedek, Davidadze, Melikson, Radi (Broun 84), Ogu, Nwakaeme, Maranhao (Sahar 69).
Damir Skomina (Slovenia).
FC Porto 1 Roma 1. Ludogorets 2 Plzen 0. Villarreal 1 Monaco 2.