The Hoops were trailing 2-0 to the Kazakhstan champions from the trip to Astana, but they treated their fans to a great European night in the east end of Glasgow.
Shakhter keeper Aleksandr Mokin made a series of good saves during the expected early onslaught but in the first of two added minutes at the end of the first half, Kris Commons thundered in a left-footed drive from 25 yards to give the home side the lead.
That deserved breakthrough was the boost needed to go and finish the job in the second half.
Greece international Georgios Samaras grabbed number two three minutes after the break to shake Celtic Park to its foundations.
As the home side went for number three to prevent extra time, striker Anthony Stokes hit the bar with a volley on the hour mark.
The Scottish champions survived a couple of scares as Shakhter tried to fight their way back into the tie but in the second minute of injury time Forrest slammed the ball high into the net from a Stokes pass to send Parkead wild and take Neil Lennon's men into Thursday's draw for the second successive season.
The goal sparked wild scenes of celebration after the final whistle as the Celtic fans once again looked forward to mixing it with Europe's elite.
The night started on a positive note for the Scottish champions.
Lennon was boosted by the return of Commons, Samaras, Stokes and Forrest who had all recovered from their respective injuries.