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PSG were facing elimination after a disappointing group stage, with three losses and a draw, but were utterly dominant against an outclassed Stuttgart side as they confirmed their place in the play-off round.
With six minutes gone, Bradley Barcola headed PSG in front. Stuttgart probed for an equaliser but PSG hit on the counter, Dembele tapping a Barcola pass into an empty net.
Always a threat on the counter, Doue, Barcola and Dembele linked up again for PSG's third.
Dembele thrashed in another superb effort shortly after half-time to snuff out Stuttgart's unlikely comeback hopes.
Stuttgart got on the scoreboard after 77 minutes when Willian Pacho scored an own goal.
The loss means Stuttgart are eliminated from the Champions League on their return to the competition after 15 years.
