Ousmane Dembele scored a hattrick as Paris Saint-Germain romped to a 4-1 win at Stuttgart, qualifying themselves for the Champions League playoffs.

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 after Desire Doue stood a cross up at the back post following a corner.

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, with the latter blasting in a rocket from the right of the goal.

Dembele thrashed in another superb effort shortly after half-time to snuff out Stuttgart's unlikely comeback hopes and keep the French side in the Champions League.

Stuttgart got on the scoreboard after 77 minutes when Willian Pacho scored an own goal, but the damage was already done, with PSG keeping their hopes of a first Champions League trophy alive.

The victory relieves the pressure on PSG coach Luis Enrique and sets the French giants up for a two-legged knockout tie in February in order to progress to the last 16.

The loss means Stuttgart are eliminated from the Champions League on their return to the competition after 15 years.

Unbeaten and with a 10-point lead atop the table in Ligue 1, PSG had struggled with a tough draw in the competition's new format.

Losses to Arsenal, Bayern Munich and Atletico Madrid, along with a home draw against PSV Eindhoven, had PSG facing an unthinkable early exit in a competition reformed to favour Europe's big guns.

Both sides knew a point would likely be enough to reach the knockouts and with PSG desperate to continue in Europe, they had fended off pre-match suggestions they may play for a draw in Germany.

Any such speculation was dispelled early when PSG energetically pressed Stuttgart into giving up a corner, with Barcola heading in a clever flick on from Desire Doue.

PSG 'keeper Gianluigi Donnarumma saved twice in quick succession from Stuttgart's Chris Fuehrich before the visitors hit back on the counter, Dembele tapping in an inch-perfect pass from Barcola after 26 minutes.

Dembele put PSG up by three 10 minutes before the break, blasting an unstoppable rocket past home goalie Fabian Bredlow.

The former Borussia Dortmund and Barcelona forward completed his hat-trick in the 54th minute, curling into the top corner.

Stuttgart pushed PSG's Pacho into an own goal with 13 minutes remaining but the effort remained just a consolation, with the visitors remaining in total control.