Neil Lennon's side, who are facing opposition from Kazakhstan for the first time, will be confident of successfully negotiating their final qualification obstacle and secure a highly sought-after berth in the group stages along side Europe's elite.
The Bhoys can take a big step towards earning a place in Thursday week's draw if they can maintain their unbeaten start to the season in the Kazakh capital but will face a stern test as their opponents aim to make history of their own.
After shocking Bate Borisov in the second qualifying round, Viktor Kumkov's men then eased past Albanian title holders KS Skenderbeu to book a date with the Bhoys and are just two games away from becoming the first club from the eastern European country to reach the Champions League group stages.
While the hosts will be able to draw on additional encouragement from a five-match unbeaten home run in Europe for the visit of their superior opponents, Celtic have the wherewithal and experience to safely negotiate the tricky ties that the qualification process throws up.
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|10/1||Celtic are 10/1 with BetVictor to beat Shakhter Karagandy 2-0 in the first leg of their play-off
However, they have had mixed fortunes in the qualifying stages in recent years and will be desperate to avoid falling at the final hurdle for the third time in four years.
The SPL champions headed straight from Pittodrie to Aberdeen Airport following Saturday's Scottish Premiership encounter with the Dons but Lennon insists that they have taken every precaution to ensure their Champions League ambitions are not ruined by travel weariness.
"It's difficult," he told reporters. "It's a six- or seven-hour flight and we arrive very early in the morning. Sunday will be important in terms of rest and recovery, getting up to speed with the time difference and getting enough nutrition and fluids into the players, so that they are not dehydrated, and also acclimatising to the weather."
Unlike their opponents, Shakhter will have no worries about fatigue or weariness ahead of the game. The Kazakh champions rested their entire team but still enjoyed a morale-boosting victory over the second-top team in the league.
Coach Viktor Kumykov admitted: "We decided to divide our squad into two groups because we have a lot of games coming up. So the players who will meet Celtic were all rested."
Meanwhile, the Shakhter boss has banned his players from speaking ahead of the game with the Scottish champions, explaining: "I would prefer if my players didn't talk to the media before playing this game. It would only serve as a distraction and could be used against them."
Their latest result gives Shakhter hope of retaining their league title and they are now in third place, three points behind leaders Aktobe.
First-choice goalkeeper Mokin, top-scorer Sergei Khizhnichenko, who were both part of the national side that defeated Georgia earlierin August, and Lithuania international Gediminas Vicius all watched from the stands at the weekend ahead of Tuesday's first leg. Also left out were captain Andrei Finonchenko and Colombia-born Roger Canas.
Meanwhile, the Hoops boss expects most of his injured players to declare themselves fit for the first leg with strikers Amido Balde and Anthony Stokes both nursing calf strains and wingers James Forrest and Derk Boerrigter struggling with ankle knocks.
Dutch centre-half Virgil van Dijk has an ongoing foot problem although he made a substitute appearance in the win over Aberdeen while Australian midfielder Tom Rogic is also expected to be fit despite ankle ligament problems.