Celtic's hopes of reaching the Champions League group stage suffered a severe blow as Shakhter Karagandy took control of their play-off tie.
The Kazakh side gained an early lead through Andrei Finonchenko's close-range finish.
Kris Commons struck the bar and Georgios Samaras headed wide as the visitors tried to force a leveller.
Emilio Izaguirre and James Forrest also threatened for Celtic before Sergey Khizhnichenko headed Shakhter's second.
Celtic will seek to overturn their deficit in next Wednesday's return meeting in Glasgow.
Celtic could not capitalise on their early chances
The first-leg fixture took place at the 30,000-seat Astana Arena in Kazakhstan's capital instead of Shakhter's smaller capacity ground in Karagandy.
And, like Celtic's previous two qualifying rounds, the Scottish champions were playing their away leg on an artificial surface.
Neil Lennon's side had secured aggregate wins against Cliftonville and Elfsborg without conceding a goal but a new defensive line-up looked vulnerable as Shakhter took the lead.
Nikola Vasiljevic headed on Gediminas Vicius' long throw-in and Finonchenko slid in to tuck the ball past goalkeeper Fraser Forster.
Earlier, Virgil van Dijk had twice threatened to mark his first Celtic start with a goal.
Aleksandr Simcevic cleared off the line after the Dutchman outmuscled keeper Aleksandr Mokin at a corner before the 22-year-old had a header saved.
And the home side had another narrow escape when Commons' superbly struck shot hit the underside of the bar and bounced back into play off the goal-line, with the officials deeming the ball had not gone in.
Neil Lennon hopeful despite Celtic's Champions League loss
Samaras headed Charlie Mulgrew's free-kick narrowly wide moments later.
Izaguirre may have done better after latching on to Commons' diagonal ball early in the second half, the full-back scooping his shot over from near the penalty spot.
Throw-ins from Vicius continued to cause Celtic problems and Shakhter's confidence in open play was evident as Khizhnichenko tested Forster at the end of a sweeping move.
And, after Mokin did well to block Forrest's header from an inviting Izaguirre cross, Khizhnichenko rose to direct Vicius' wayward shot past Forster.
Celtic's late push for an away goal proved fruitless with Mulgrew unable to keep his header down in injury time.
Shakhter will now travel to Celtic Park hopeful of reaching the group stages of the competition for the first time, while Lennon's men will drop into the Europa League if they cannot recover the deficit.
Free kick awarded for an unfair challenge on Georgios Samaras by Aleksandar Simcevic. Charlie Mulgrew restarts play with the free kick.
Header at goal by Charlie Mulgrew goes over the bar.
Unfair challenge on Joe Ledley by Sergey Khizhnichenko results in a free kick. Free kick taken by Fraser Forster.
Gediminas Vicius crosses the ball. Charlie Mulgrew manages to make a clearance.
Foul by Serhiy Malyi on Kris Commons, free kick awarded. Strike on goal comes in from Virgil van Dijk from the free kick and goes over the bar.
Corner from the right by-line taken by Gevorg Ghazaryan. Amido Balde manages to make a clearance.
Substitution Emilio Izaguirre leaves the field to be replaced by Amido Balde.
Substitution Igor Zenkovich on for Andrei Finonchenko.
Free kick awarded for a foul by Sergey Khizhnichenko on Adam Matthews. Free kick crossed by Charlie Mulgrew. Alexandr Mokin punches the ball.
A cross is delivered by Adam Matthews. Clearance by Aleksandar Simcevic.
Centre by James Forrest. Aldin Dzidic makes a clearance.
Assist on the goal came from Gediminas Vicius.
76:26 Goal scored
Goal! - Sergey Khizhnichenko - Karagandy 2 - 0 Celtic Sergey Khizhnichenko grabs a goal with a headed effort. Shakhtyor Karaganda 2-0 Celtic.
Charlie Mulgrew produces a cross. Serhiy Malyi makes a clearance.
Free kick awarded for a foul by Andrei Finonchenko on James Forrest. James Forrest restarts play with the free kick.
Virgil van Dijk gives away a free kick for an unfair challenge on Sergey Khizhnichenko. Andrei Finonchenko crosses the ball in from the free kick. Fraser Forster gets a fist to the ball to punch .
Free kick awarded for an unfair challenge on Scott Brown by Andrei Finonchenko. Scott Brown takes the free kick.
The ball is swung over by Emilio Izaguirre. James Forrest takes a shot. A parry by Alexandr Mokin prevents the goal.
Steven Mouyokolo fouled by Sergey Khizhnichenko, the ref awards a free kick. Free kick taken by Steven Mouyokolo.
Shot by James Forrest went wide of the right-hand post.
Serhiy Malyi concedes a free kick for a foul on Kris Commons. Free kick crossed by Charlie Mulgrew. Nikola Vasiljevic makes a clearance.
Substitution Adam Matthews is brought on as a substitute for Mikael Lustig.
Mikael Lustig crosses the ball. Georgios Samaras takes a shot.
Sergey Khizhnichenko takes a shot. Fraser Forster safely holds on.
A cross is delivered by Scott Brown. Aldin Dzidic manages to make a clearance.
Charlie Mulgrew takes the chance to get an effort at goal. Alexandr Mokin safely holds on.
A cross is delivered by Sergey Khizhnichenko.
Free kick awarded for an unfair challenge on Roger Canas by Scott Brown. Gevorg Ghazaryan takes the free kick.
Aleksandar Simcevic has an effort at goal and missed to the left of the net.
Free kick awarded for a foul by Virgil van Dijk on Sergey Khizhnichenko. Andrei Finonchenko crosses the ball in from the free kick.
Emilio Izaguirre sends in a cross. Nikola Vasiljevic manages to make a clearance.
Emilio Izaguirre takes a shot.
The ball is crossed by Charlie Mulgrew.
Mikael Lustig produces a cross. Aleksandar Simcevic manages to make a clearance. Corner taken by Kris Commons. Kris Commons produces a cross.
Free kick awarded for an unfair challenge on Emilio Izaguirre by Serhiy Malyi. Georgios Samaras takes the free kick.
Corner taken by Charlie Mulgrew. Nikola Vasiljevic manages to make a clearance.
The referee starts the second half.
45:00 +0:55 Half time
Half Time The referee blows for half time.
Steven Mouyokolo challenges Andrei Finonchenko unfairly and gives away a free kick. Andrei Finonchenko restarts play with the free kick.
The referee shows Steven Mouyokolo a yellow card for unsporting behaviour.
45:00 +0:20 Booking
Emilio Izaguirre sends in a cross. Alexandr Mokin gets a fist to the ball to punch .The ball is swung over by Emilio Izaguirre. Nikola Vasiljevic manages to make a clearance. Sergey Khizhnichenko takes a shot and went wide right of the net.
Emilio Izaguirre sends in a cross. Clearance by Serhiy Malyi. Joe Ledley takes a shot.
The ball is crossed by Scott Brown.
Kris Commons fouled by Andrei Finonchenko, the ref awards a free kick. James Forrest takes the free kick. The ball is crossed by Kris Commons. Serhiy Malyi gets a block in. Corner from the left by-line taken by Charlie Mulgrew. Foul by Virgil van Dijk on Aldin Dzidic, free kick awarded. Alexandr Mokin takes the free kick.
Unfair challenge on James Forrest by Roger Canas results in a free kick. Mikael Lustig takes the free kick.
The ball is swung over by Gediminas Vicius. Clearance by Virgil van Dijk.
Roger Canas takes a shot.
Kris Commons takes a shot. Blocked by Serhiy Malyi.
The ball is sent over by Gevorg Ghazaryan. Virgil van Dijk manages to make a clearance. Gediminas Vicius takes the chance to get an effort at goal. Fraser Forster safely holds on.
The ball is crossed by James Forrest.
Corner taken by Gevorg Ghazaryan. Header at goal by Nikola Vasiljevic goes over the bar.
Georgios Samaras fouled by Serhiy Malyi, the ref awards a free kick. Charlie Mulgrew sends in a cross. Header at goal by Georgios Samaras goes right of the post.
Foul by Scott Brown on Andrei Finonchenko, free kick awarded. Andrei Finonchenko takes the free kick. The ball is sent over by Aleksandar Simcevic. Header by Serhiy Malyi goes over the bar.
The ball is crossed by Emilio Izaguirre. Header by Kris Commons goes over the bar.
Kris Commons takes a fantastic shot and strikes the bar.
Corner from the left by-line taken by Andrei Finonchenko.
Roger Canas takes the chance to get an effort at goal and missed to the left of the net.
Charlie Mulgrew sends in a cross. James Forrest produces a cross. Emilio Izaguirre produces a cross. Clearance by Aleksandar Simcevic. Emilio Izaguirre delivers the ball. Nikola Vasiljevic makes a clearance.
Assist by Nikola Vasiljevic.
11:21 Goal scored
Goal! - Andrei Finonchenko - Karagandy 1 - 0 Celtic Andrei Finonchenko grabs a goal with a left foot finish. Shakhtyor Karaganda 1-0 Celtic.
Gediminas Vicius produces a cross.
Kris Commons has an effort at goal and missed to the right of the net.
The ball is delivered by Charlie Mulgrew. Clearance made by Aldin Dzidic.
Corner taken by Charlie Mulgrew from the left by-line.
The ball is swung over by Mikael Lustig. Gediminas Vicius makes a clearance.
Corner taken by Kris Commons from the left by-line. Steven Mouyokolo takes a shot. Alexandr Mokin parries the ball away.
Emilio Izaguirre crosses the ball. Andrey Poryvaev makes a clearance. Corner taken by Charlie Mulgrew from the right by-line. Parried by Alexandr Mokin back into danger.
Georgios Samaras is caught offside. Free kick taken by Aldin Dzidic.
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