Manager Neil Lennon had bemoaned the international fixture schedule that saw many of his players return to Glasgow less than 48 hours before their lunchtime clash at in-form Aberdeen.
And his squad suffered further disruption less than 12 hours before kick-off when a fire alarm went off at their hotel.
Celtic started slowly at Pittodrie although the home side could not make the most of some decent opportunities to put the ball in the box, but they got a grip of possession before the key moment just before the break when Aberdeen goalkeeper Jamie Langfield was sent off for conceding a penalty that Kris Commons tucked away.
Celtic, who scored late on through James Forrest, embarked on the seven-hour flight to Astana from Aberdeen Airport immediately after the match to give themselves as much preparation time as possible before Tuesday afternoon's first leg with Shakhter Karagandy.
But they should be able to cope with whatever comes their way in the former Soviet state after brushing off their late-night disruption in the Granite City.
Lennon said: "It's becoming a bit of regular occurrence in Aberdeen. The fire alarm went off about half one. It was freezing outside as well. I think it was somebody playing a prank but
for some of the residents in the hotel it wasn't very nice.
"There were a couple of elderly people and people in wheelchairs who were a little bit distraught. It is tiresome but it can also fire you up."