Andre Schuerrle puts Chelsea ahead at Stamford Bridge last night.

Chelsea substitute Demba Ba struck a dramatic late goal to seal a 2-0 home victory over Paris St Germain and a place in the Champions League semi-finals on the away goals rule last night.

Lacklustre Real Madrid edged past Borussia Dortmund 3-2 on aggregate after slumping to a 2-0 defeat to advance to the last four and stay on track for their tenth crown.

PSG were heading for a first appearance in the last four since 1995 when Ba bundled in a loose ball after 87 minutes to clinch the tie, which ended 3-3 on aggregate.

Chelsea went ahead in a tense end-to-end battle at Stamford Bridge with a superbly-taken goal from substitute Andre Schuerrle after 32 minutes and they also hit the bar twice in two minutes early in the second half.

PSG, who won the first leg 3-1, dominated early on and Edinson Cavani missed two good chances in the closing stages which added to the almost unbearable tension on the night.

Chelsea, despite losing playmaker Eden Hazard to injury after 17 minutes when Schuerrle came on, finished strongly and were worthy winners on another memorable European night in west London.

Schuerrle scored just as Chelsea were establishing themselves following an opening half-an-hour in which PSG looked the more organised, composed and quicker side.

But despite looking the better side, PSG did not trouble Chelsea keeper Petr Cech and the first real chance came at the other end where visiting keeper Salvatore Sirigu needed a late leaping dive to keep out a deflected Frank Lampard free-kick.

Four minutes after that Chelsea did score when Germany international Schuerrle, left unmarked in front of goal, executed a great delivery to put the hosts ahead.

Chelsea visibly gained in confidence after the goal and they started the second half stronger too, twice coming close to extending their lead on the night within 10 minutes of the break with two efforts that struck the bar.

The first came from Schuerrle whose powerful curler left Sirigu stranded but bounced back into play. Within a minute PSG conceded a free-kick just outside the box with Oscar cracking the ball against the bar with his effort.

Cavani had two good chances to at least gain a draw for his side but Ba did get on the scoresheet which was enough to put Chelsea through and send manager Jose Mourinho racing down the touchline to where his players were celebrating.

In Germany, two first-half goals by Marco Reus, both coming from Real mistakes, gave Dortmund a deserved lead as the Spaniards, who had a penalty saved in the 17th minute, were left mesmerised by the Germans' frantic pace.

Real, with top scorer Cristiano Ronaldo left on the bench due a minor knee injury, saw their 3-0 advantage from the first leg in Madrid almost evaporate in a disastrous first half for them.

Real briefly recovered in the second half before the Germans, last season’s runners-up, again surged forward, missing half a dozen clear scoring chances and also hitting the post.

“That was too much suffering and I think it was deserved,” said Real keeper Iker Casillas.

“But from time to time it’s good to have this kind of wake up call that reminds us it’s not always easy, and especially not in the Champions League.

“It is better that it happened in this game than in the decisive matches to come. We had to show quite a lot of mental strength because going 2-0 down by the 37th minute there were a lot of things going through our heads.”

Quarter-finals, second legs