Paris St Germain exited the Champions League at the semi-final stage as a Mats Hummels goal earned Borussia Dortmund a 1-0 win at the Parc de Princes to send them through 2-0 on aggregate.

Hummels headed in from a corner at the start of second half, moments after PSG had wasted a golden chance to level the tie when Warren Zaire-Emery crashed the ball against the post from close range.

It was one of four occasions on the night when Luis Enrique’s side struck the woodwork. In the end, they paid for their wastefulness in front of goal across the two legs, failing to score form 45 attempts, as Edin Terzic’s clinical visitors dug in to reach their third final where they will face either Real Madrid or Bayern Munich on June 1.

In a first half starved of clear openings, the game almost broke open for both sides after 35 minutes. First Kylian Mbappe was prevented from reaching Fabian Ruiz’s cut-back by a superb interception from Hummels, the defender sliding in to nick the ball away from the France international as he waited to pounce 10 yards from goal.

Dortmund broke, and in a flash Karim Adeyemi was running at an exposed PSG defence. Advancing into the penalty area, he drew back his left foot and fired low only to be denied by a strong palm thrust out brilliantly by Gianluigi Donnarumma.

Earlier, Ousmane Dembele had lashed high and wide at the near post after Mbappe’s burst infield had taken three Dortmund players out of the game.

On the whole, it was a first period in which the visitors contained the threat of PSG and doggedly guarded their lead in the tie.

Enrique’s team should have led in the first moments of the second half. Mbappe’s cross flicked off the head of Marcel Sabitzer, Goncalo Ramos reached for it and turned into the path of Zaire-Emery, who lashed it against the post.

Within minutes they were made to rue their profligacy in the tie. From Julian Brandt’s corner, Hummels cleverly stepped away from his marker Lopes Beraldo and thumped his header at the back post beyond Donnarumma.

Ramos lifted a shot over the bar from Vitinha’s square ball as PSG sought a riposte, before Nuno Mendes came within a whisker of levelling when he rattled the woodwork with a ripping long-range drive.

A breathless match took another twist when the referee pointed to the penalty spot after Dembele was tripped by Hummels, only to immediately commute the award to a free-kick, VAR confirming the contact happened fractionally outside the box.

Mbappe struck the bar after a goalmouth scramble with five minutes to play before Vitinha did likewise with a blistering drive.

Enrique’s side battled to the end, but as so often in this competition they ultimately came up short as Dortmund celebrated.