Skipper Scott Brown returned to the team as did the impressive Sefan Johansen. Mulgrew partnered Boyata in the centre of the rearguard with a view to the Stjarnan tie which Van Dijk will miss through suspension after his ridiculous red card against Inter Milan last season.
Hanousek claimed the opening goal in the 13th minute when he snapped up a rebound off Boyata to drill a low shot past Gordon at his left hand side.
In the 27th minute, Griffiths thumped in a well-placed penalty-kick after Lustig had been pushed in the back by a reckless Czech defender.
Dukla restored their advantage in the 36th minute with Hanousek again on target when he converted a cross from the right. A couple of minutes later he almost claimed a hat-trick, but he hit the crossbar with a superb curling effort.
Two minutes from half-time, Celtic were back on level terms when Mackay-Steven raced onto a neat Johansen ball to tuck a low effort beyond the exposed keeper.
However, Hanousek was not to be denied and he claimed his third goal via the penalty spot in the 49th minute after a foul from Mulgrew was punished by referee John Beaton.
Ten minutes later, Fasan was beaten again when Jakub Mares sent a glancing header from a right wing cross soaring high into the top corner.
With seven minutes left, Van Dijk headed the Hoops’ third goal after an accurate right-wing free-kick delivery from Johansen, but two minutes later Tomas Prikryl hit his side’s fifth goal with a low drive that eluded Fasan at his far post.
A word here about the young Italian keeper. Coach Steve Woods has got to work on his distribution because it didn’t look too clever on this occasion.
Celtic return to Paisley on Friday to face Davie Moyes’ Real Sociedad.
Deila started with his line-up: Gordon; Lustig, Boyata, Mulgrew, Izaguirre; Brown, Rogic; Forrest, Johansen, Mackay-Steven; Griffiths. The subs were: Fasan, Fisher, Ambrose, O’Connell, Van Dijk, Tierney, Henderson, Lindsay, Nesbitt, Donnelly, Stokes, Scepovic, Trialist, Thomson, Boerrigter, Hazard.