The diminutive attacker fired home in the second minute of injury-time after some sublime approach play by Anthony Stokes to clinch a 3-2 success on aggregate.
The Scottish champions had trailed 2-0 from the first-leg but reduced the arrears on the stroke of half-time through Kris Commons' blockbuster.
And they pulled level in the tie just three minutes after the restart courtesy of Georgios Samaras' composed finish.
Both sides then had chances to turn the contest in their favour, with Stokes crashing the bar with a volley and Sergei Khizhnichenko smacking the woodwork for the visitors.
However, it was Celtic who finally got the match-winning strike deep in injury-time as Neil Lennon's team earned a deserved place in Friday's draw for the group stage.
5’ CHANCE – Aleksandr Mokin pulls off a stunning stop to keep out Mikael Lustig's goalbound header following a pinpoint centre by Commons on the right.
12' CHANCE - Mokin continues to almost single-handedly keep Celtic at bay, producing another sensational save to palm away Anthony Stokes' bouncing header.
45+1' GOAL! - CELTIC 1-0 SHAKHTER. What a goal! Commons takes the ball off Samaras 25 yards from goal and unleashes a stunning shot that arrows into the corner. Game on.
48' GOAL! - CELTIC 2-0 SHAKHTER. Samaras levels the tie. A corner is only half-cleared and when an attempted shot falls for the big Greek, he shows great composure to take a touch and fire past the keeper from 10 yards.
60' OFF THE BAR! A fantastic run from Forrest on the left ends with a delicious cross that Stokes meets on the volley, but his effort crashes back off the woodwork.
63' OFF THE BAR! Vicius' long throw causes Celtic all sorts of problems once again and they are so lucky to survive as the ball cannons back off the crossbar via a touch off Khizhnichenko.
90+2' GOAL! - CELTIC 3-0 SHAKHTER. Forrest fires in a sensational last-gasp winner after some superb approach play by Stokes on the left side of the area.
Celtic have now managed to overturn a 2-0 first-leg deficit in Europe on four of the five occasions they have been faced with the task at Celtic Park.
Celtic have won seven of their last nine European fixtures in Glasgow.
Shakhter can still look forward to an historic first European group stage appearance for a Kazakh club, as they advance to the equivalent phase of the Europa League.
TALKING POINT - New signings. So far Celtic have struggled to make any significant inroads on the transfer market, but with the promise of Champions League football on offer, don't be surprised to see Lennon doing some serious business over the next few days as he bids to make his side competitive ahead of the group stage.
MAN OF THE MATCH
Georgios Samaras (Celtic): The big Greek scored one and was a constant menace throughout.
CELTIC: Forster 6, Matthews 6, Ambrose 6, Lustig 7, Mulgrew 7, Forrest 7, Brown 7, Ledley 7, Commons 8, Samaras 8, Stokes 7. Subs: Boerrigter 6, Van Dijk 5.
SHAKHTER KARAGANDY: Mokin 8, Vasiljevic 6, Poryvaev 7, Dzidic 7, Maliy 6, Simcevic 6, Vicius 6, Ghazaryan 6, Canas 6, Finonchenko 6, Khizhnichenko 6. Subs: Zenkovich 6,
- Sports & Recreation
- Anthony Stokes
- Georgios Samaras
- Kris Commons
- Celtic Park
- James Forrest
- Aleksandr Mokin