Pavel Nedved and David Trezeguet had given Juventus two potentially crucial away goals after defender Christian Schulz had opened the scoring for Werder.
When Tim Borowski put the German side level, in the 87th minute of a pulsating match, a 2-2 draw looked likely.
Two minutes into injury-time, however, Micoud popped up with a header from a corner that rebounded off Alessandro Del Piero, on the goalline, and into the net - sending the 37,000 crowd at the packed Weserstadion into wild celebrations.
Werder arguably deserved their victory after making the early running.
Schulz had converted Werder’s domination of the first half into a goal on 39 minutes, when the defender found the net for the first time this season after the Juve defence made a mess of trying to clear the ball following a clever backheel from Ivan Klasnic.
But former European Footballer of the Year Nedved ended an otherwise anonymous performance as the Czech collected a superb pass from Patrick Vieira to shoot high into the net on 73 minutes.
Werder were rocked, and from unpromising beginnings, Del Piero’s cross bobbled off Werder’s Brazilian defender Naldo and was headed in by unmarked French striker Trezeguet with 82 minutes gone.
But the Germans were not dead, as Borowski nipped in front of Lilian Thuram to poke the ball past Gianluigi Buffon for the equaliser, before Micoud’s late goal gave Werder a chance of reaching the last eight.
The home side could easily have scored three times in what was a highly attacking first half.
On 23 minutes, a volley from the unmarked Torsten Frings was turned around the post by Buffon, who then produced an even better save from Frank Fahrenhorst’s header.
Juventus broke away, but Zlatan Ibrahimovic shot wide when he had only goalkeeper Tim Wiese to beat, although the assistant referee had raised his flag for offside.
After Schulz scored, Wiese denied Trezeguet and rushed off his line to thwart Vieira.
: Wiese, Owomoyela, Fahrenhorst, Naldo, Schulz, Frings, Baumann, Borowski, Micoud, Klose (Haedo Valdez 68), Klasnic.
: Buffon, Blasi, Thuram, Cannavaro, Balzaretti, Camoranesi (Zalayeta 76), Emerson, Vieira, Nedved, Trezeguet, Ibrahimovic (Del Piero 59).
: Manuel Gonzalez (Spain).