Former Liverpool manager, 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 extent to match a brilliant and madcap European night at Celtic Park.