Brendan Rodgers' side appeared to have one foot in the group stage when a ninth-minute Tom Rogic goal and Griffiths' double were just reward for a dazzling display during the opening 45 minutes.
But, not for the first time in his career, Rodgers watched a side under his direction display defensive vulnerabilities and puncture the confidence established through slick attacking work.
Lucio Maranhao scored in the 55th minute to crown a break from a Celtic corner and Maor Melikson struck two minutes later, as seething Hapoel boss Barak Bakhar was seemingly rewarded for spending most of the half-time break alone in the away dugout.Rodgers refused to deviate from his expansive approach and substitute Moussa Dembele capitalised on poor goalkeeping from David Goresh before captain Scott Brown restored the three-goal cushion three minutes from time.
Rodgers has warned that his side must improve defensively and not get carried away after this win.
"We're nowhere near the finished article yet but they look an exciting team full of character. I thought the fans were absolutely incredible as well. The support tonight really helped the players.
"When it went to 3-2, before this it might have been an edgy game but they stayed calm and roared the team on. In the main, we defended well but we must be better - we have to be better, and that will come with more work."Elsewhere, in Spain, Alexandre Pato continued his extraordinary record of scoring on his debuts as he struck in Villarreal's 2-1 defeat to
Jordan Hypervenom Phantom II 10-man Monaco in the first leg of their Champions League qualifying play-off.
The forward, who has previously netted in his maiden appearances for Inter, AC Milan, Corinthians, Chelsea and Brazil, opened his Villarreal account 36 minutes into his
ace 16+ purecontrol cleat El Madrigal bow, restoring parity following Fabinho's earlier penalty.
However, the LaLiga side - now
adidas x sliver managed by Fran Escriba following Marcelino's departure -
superfly v black cleat could not build on Pato's leveller, with Portugal playmaker Bernardo Silva doing the damage for Monaco, who had Benjamin
magista obra black cleat Mendy sent off late on.