Real Madrid have booked their spot in the semi-finals of the Champions League after recording a 4-2 victory over Bayern Munich in the second leg of their quarter-final at the Bernabeu on Tuesday night.

Ten-man Bayern led 2-1 after 90 minutes to force extra time after Real Madrid's success by the same scoreline at the Allianz Arena last week, but Cristiano Ronaldo's second of the night in the 105th minute effectively decided the tie.

Ronaldo then completed his hat-trick in the second period of extra time as the Portugal international registered his 100th goal in the Champions League, before substitute Marco Asensio made it 4-2 on the night late on.

A calf problem kept Gareth Bale on the sidelines, meaning that Isco joined Ronaldo and Karim Benzema in the final third for Real Madrid, while it was again Nacho alongside Sergio Ramos in central defence.

As for Bayern, Robert Lewandowski was back in the team after recovering from a shoulder problem, while Mats Hummels's return from an ankle injury came at the perfect time due to Javi Martinez's suspension.

It was the visitors that had the first serious chance of the match in the ninth minute, but Arjen Robben, after being given the freedom of the Real Madrid penalty box, could only bounce his effort over the crossbar from close range in an early warning for Zinedine Zidane's side.

Bayern continued to dominate as the first period gathered pace, and Arturo Vidal sent a long-range effort over the Real Madrid crossbar in the 13th minute as the home side struggled for possession of the ball against the German champions.

Real Madrid's first opportunity of the match did not arrive until the 24th minute when Marcelo broke down the left before picking out the head of Benzema with a smart cross, but the Frenchman's effort was wide of the post.

Spanish full-back Dani Carvajal then came close for the home side after striking a powerful effort towards the bottom corner, but Manuel Neuer was on hand to make a wonderful save in the Bayern goal.

Moments later, the Madrid outfit had another opportunity when Ramos pounced on a loose ball inside the Bayern box, but Jerome Boateng cleared his fellow centre-back's effort off the line as it somehow remained goalless at the Bernabeu.

Ten minutes before the break, Toni Kroos had a super chance to send Real Madrid ahead against his former club, but the German international missed Neuer's crossbar, before Ronaldo stung the palms of the Bayern goalkeeper moments later.

Bayern continued to threaten on the counter-attack in the latter stages of the first period, although it was Real Madrid that looked the team more likely to open the scoring, and only a wonderful block from Hummels prevented Kroos's close-range effort from causing Neuer all sorts of problems.

A wonderful defensive clearance from Marcelo prevented Robben from sending Bayern ahead early in the second period, but the German champions were awarded a penalty in the 51st minute when Robben went down in the box under a clumsy challenge from Casemiro.

Vidal missed from the spot last week, but Lewandowski made no mistake at the Bernabeu as the returning striker sent the ball past Keylor Navas to send Bayern into a 1-0 lead on the night.

Vidal should have scored a second for the visitors less than two minutes later after being found unmarked inside the Real Madrid box, but the Chilean somehow scooped his effort over the crossbar from close range, before Franck Ribery brought a smart save from the Real Madrid goalkeeper just before the hour.

Asensio for Benzema was Real Madrid's first change of the match in the 64th minute, which led to Ronaldo going through the middle as Zidane looked for the tonic to upset a dominant Bayern.

Douglas Costa was Bayern's first substitute 20 minutes from time, with the alteration occurring during a period where Real Madrid had managed to stem the flow of pressure with a spell of possession.

It was an end-to-end game in the 75th minute as both teams committed players in the final third of the field, and Thomas Muller was next off the Bayern bench as the Germans desperately looked for a second goal.

When Ronaldo headed a Casemiro pass into the Bayern net in the 76th minute, Real Madrid had some insurance in the tie, but Bayern incredibly took a 2-1 lead less than two minutes later when Ramos bizarrely turned into his own net after a mix-up in the home side's defence.

The tie then turned in Real Madrid's favour in the 84th minute when Vidal picked up his second yellow card for a late challenge on Asensio, leaving Bayern with 10 men against Los Blancos for the second successive match.

Lewandowski had to be replaced in the 88th minute after putting in a long shift carrying a shoulder problem, and Bayern survived some late pressure from the home side to force an additional 30 minutes.

Ronaldo came close to sending Real Madrid ahead in the tie in the seventh minute of extra time when he struck a powerful effort from distance, but Neuer was on hand to make another smart save, before the German goalkeeper made an even better stop to deny Asensio two minutes later.

Bayern could not hold on, however, and Real Madrid scored their second of the night in the 105th minute when Ronaldo collected a sweeping pass from Ramos before firing into the bottom corner. Replays though showed that the Portuguese was in an offside position in what was a bitter pill for the visitors to swallow.

Ronaldo then completed his hat-trick in the 110th minute after tapping a Marcelo cross into the back of the net, before a brilliant individual goal from Asensio two minutes later made it 4-2 on the night and 6-3 on aggregate as Real Madrid joined their rivals Atletico Madrid in the semi-finals of the competition.