Substitute Georgios Samaras scored in injury-time in Russia to send Celtic through to the final round of Champions League qualifying.
At 1-0 down from the home leg, Celtic needed to win away in Europe for the first time in 23 matches since 2003.
After a stale start, striker Scott McDonald headed the first from Andreas Hinkel's cross just before the break.
Hinkel cleared twice off the line, before Samaras weaved across the box to squeeze a low shot inside the post.
The win rewrites club history by overturning a first-leg defeat for the first time, as well as ending their well-documented poor away European record.
With so much at stake, the early exchanges were even, with both sides appearing to struggle with control on what looked like a dry, sticky surface.
As the match was largely bogged down in the midfield, almost 10 minutes passed before the first effort on goal from either side, although Alexander Kerzhakov's weak snap-shot did not trouble Artur Boruc in the Celtic goal.
But with Aiden McGeady looking lively on the right wing, the visitors came more into the match as the first half was drawing to a close.
Landry N'Guemo managed a rare shot on goal which bounced harmlessly into the arms of Dinamo keeper Vladimir Gabulov.
And with a minute of the first period remaining Celtic made the vital breakthrough from a McDonald header.
After good play from N'Guemo and Marco Antoine-Fortune, Hinkel fired in a deep cross to the back post where the diminutive Australian striker nodded the ball downward past Gabulev to level the tie from six yards.
Moments later, Hinkel was on hand to hook the ball away from the goal when home captain Dmitri Khokhlov fired in a low effort on the volley. But the visitors went in at half-time with their valuable lead intact.
Dinamo had the bit between their teeth after the restart and Hinkel was almost punished when he failed to control the ball across the edge of the penalty area, allowing Viktor Svezhov to drive in a first-time shot inches past the post.
Kirill Kombarov had a decent claim for a penalty waved away when fell in the box with Danny Fox in close attendance.
And Hinkel again turned up of the goal line to keep the tie level, thumping Dmitri Kombarov's header clear with Boruc beaten.
Tony Mowbray's side applied more pressure throughout the last quarter of the game but were met with stiff banks of Dinamo resistance
Shaun Maloney appeared to have blown Celtic's chances of regulation-time victory with 30 seconds of the match to play, when he was snuffed out by the onrushing Gabulov.
But Samaras scored a dramatic second goal in added-time to record a famous win for the Glasgow club.
Dinamo Moscow: Gabulov, Kowalcyzk, Fernandez, Kolodin, Granat, Kirill Kombarov, Khokhlov, Wilkshire, Svezhov, Dmitri Kombarov, Kerzhakov.
Subs: Shunin, Smolov, Dimidko, Tanasijevic, Ropotan, Denisov, Kokorin.
Celtic: Boruc, Hinkel, Caldwell, Loovens, Daniel Fox, McGeady, Donati, N'Guemo, Maloney, McDonald, Fortune.
Subs: Zaluska, Scott Brown, O'Dea, Caddis, Crosas, Killen, Samaras.
Referee: Jonas Eriksson (Sweden)
At 1-0 down from the home leg, Celtic needed to win away in Europe for the first time in 23 matches since 2003.
After a stale start, striker Scott McDonald headed the first from Andreas Hinkel's cross just before the break.
Hinkel cleared twice off the line, before Samaras weaved across the box to squeeze a low shot inside the post.
The win rewrites club history by overturning a first-leg defeat for the first time, as well as ending their well-documented poor away European record.
With so much at stake, the early exchanges were even, with both sides appearing to struggle with control on what looked like a dry, sticky surface.
As the match was largely bogged down in the midfield, almost 10 minutes passed before the first effort on goal from either side, although Alexander Kerzhakov's weak snap-shot did not trouble Artur Boruc in the Celtic goal.
But with Aiden McGeady looking lively on the right wing, the visitors came more into the match as the first half was drawing to a close.
Landry N'Guemo managed a rare shot on goal which bounced harmlessly into the arms of Dinamo keeper Vladimir Gabulov.
And with a minute of the first period remaining Celtic made the vital breakthrough from a McDonald header.
After good play from N'Guemo and Marco Antoine-Fortune, Hinkel fired in a deep cross to the back post where the diminutive Australian striker nodded the ball downward past Gabulev to level the tie from six yards.
Moments later, Hinkel was on hand to hook the ball away from the goal when home captain Dmitri Khokhlov fired in a low effort on the volley. But the visitors went in at half-time with their valuable lead intact.
Dinamo had the bit between their teeth after the restart and Hinkel was almost punished when he failed to control the ball across the edge of the penalty area, allowing Viktor Svezhov to drive in a first-time shot inches past the post.
Kirill Kombarov had a decent claim for a penalty waved away when fell in the box with Danny Fox in close attendance.
And Hinkel again turned up of the goal line to keep the tie level, thumping Dmitri Kombarov's header clear with Boruc beaten.
Tony Mowbray's side applied more pressure throughout the last quarter of the game but were met with stiff banks of Dinamo resistance
Shaun Maloney appeared to have blown Celtic's chances of regulation-time victory with 30 seconds of the match to play, when he was snuffed out by the onrushing Gabulov.
But Samaras scored a dramatic second goal in added-time to record a famous win for the Glasgow club.
Dinamo Moscow: Gabulov, Kowalcyzk, Fernandez, Kolodin, Granat, Kirill Kombarov, Khokhlov, Wilkshire, Svezhov, Dmitri Kombarov, Kerzhakov.
Subs: Shunin, Smolov, Dimidko, Tanasijevic, Ropotan, Denisov, Kokorin.
Celtic: Boruc, Hinkel, Caldwell, Loovens, Daniel Fox, McGeady, Donati, N'Guemo, Maloney, McDonald, Fortune.
Subs: Zaluska, Scott Brown, O'Dea, Caddis, Crosas, Killen, Samaras.
Referee: Jonas Eriksson (Sweden)
