Real Madrid 4-2 Bayern Munich (agg 6-3) AET: Cristiano Ronaldo hat-trick fires Real through

Cristiano Ronaldo's hat-trick helped Real Madrid battle past 10-man Bayern Munich and into the Champions League semi-finals, with a 4-2 extra-time win (6-3 on aggregate) in an epic encounter at the Bernabeu.

Needing to score at least twice to go through after a 2-1 defeat in the first leg of the quarter-final tie, Bayern struck the first blow on Tuesday night with a Robert Lewandowski penalty shortly after half-time.

Sergio Ramos' own goal sent the game into extra-time after Ronaldo - who became the first player to reach 100 Champions League goals - had levelled on the night for Real.

The turning point, though, was when Arturo Vidal received a second yellow card late on to leave Bayern a man light, and Ronaldo capitalised with two more goals, the first of which was scored from an offside position, before substitute Marco Asensio completed the scoring with a fourth for Real.

The Spanish giants now head into the final four of the competition, their seventh straight semi-final, while Bayern fall at their earliest stage since 2009.

It was Bayern who started the sharper at the Bernabeu, and they would have opened the scoring after nine minutes were it not for an excellent piece of defending by Marcelo, who managed to scamper across to deny Thiago Alcantara from close range with a crucial last-ditch block.

Real worked their way into the ascendancy as the half dragged on, and created a couple of great chances to take the lead. First, Ramos saw a shot cleared off the line by Jerome Boateng, before Ronaldo raced in behind and hit a shot straight at Manuel Neuer - when he could have squared across for Karim Benzema in the better position.

Bayern regained the momentum after the break, but were denied again by Marcelo after 50 minutes, who was alert enough to race back onto his line to keep out Arjen Robben's chipped effort. The Dutchman did make the difference shortly afterwards, however, as he was tripped by Casemiro in the box and Lewandowski stepped up to slot the resulting penalty.

Casemiro then took it upon himself to make up for conceding the spot kick, as he created the goal which levelled the game on the night with 15 minutes of normal time remaining, clipping a fine ball into the box for Ronaldo to head home his first, adding to the two he scored last week at the Allianz Arena.

That was not to be the end of the drama. The tie turned on its head again in the 84th minute as Vidal was shown a second yellow card for a challenge on Asensio and left Bayern with 10 men, despite the Chilean - who had scored and missed a penalty in the first leg - appearing to take the ball before the man.

It was Real who struck the killer blow on the stroke of the break in extra-time. Again, though, it was a decision that went their way as Ronaldo picked up the ball in an offside position in the box before punting past Neuer.

And that was that for Bayern, who saw Ronaldo complete a perfect hat-trick later in extra-time before Asensio rushed through to add insult to injury with Real's fourth of the night.