Cristiano Ronaldo’s fifth Champions League hat-trick has inspired Real Madrid to a 3-0 comeback victory over VfL Wolfsburg to reach the semi-finals for a sixth successive season, while Manchester City are into the last four for the first time.

The 10-times European champions, 2-0 down from the first leg, made a perfect start on Tuesday with the prolific Portuguese tapping in Daniel Carvajal’s cross after 16 minutes and heading a second goal less than a minute later from Toni Kroos’ corner.

• Socceroos draw Japan on road to Russia 2008 
• The offensive Gumtree ad that inspired A-League glory

Ronaldo capped a 3-2 win on aggregate when he curled in a free-kick after 77 minutes, his 16th goal in this season’s competition and just one shy of his record 17 in 2013-14.

He also equalled Barcelona rival Lionel Messi’s record of five Champions League trebles.

“For those who doubted Ronaldo, he has vindicated himself again,” Real defender Sergio Ramos said. “We need him.”

Real have a reputation for great fightbacks but have not overturned a first-leg deficit in the Champions League since 2002, beating Bayern Munich 2-0 after a 2-1 reverse.

Wolfsburg coach Dieter Hecking told Sky Sport: “It is annoying to lose through two goals from set-pieces”.

“At this level, small things decide things. I was satisfied with phases of our game but, in the end, we didn’t have the punch,” he said.

Manchester City advanced to the semi-finals on Tuesday after a superb curling shot from Kevin de Bruyne gave them a 1-0 second-leg win over Paris St Germain to seal a 3-2 aggregate victory.

The Belgian picked his spot perfectly with 14 minutes remaining, firing past goalkeeper Kevin Trapp as PSG went out at the quarter-final stage for the fourth successive season.

City should have taken the lead at the Etihad Stadium in the first half when Trapp brought down Sergio Aguero to concede a penalty, but the Argentine fired his spot-kick wide.

City would have advanced on the away-goals rule if the game had finished 0-0 or 1-1 following last week’s 2-2 draw in Paris.

“Kevin de Bruyne is an important player for us – we deserved a goal before he scored. We dominated that game from the beginning until the end,” City manager Manuel Pellegrini told BT Sport.

“It feels great. We played a very good game.

“PSG didn’t create a lot and I think we deserved to go through. We are in the semi-finals – anything can happen. It will be tough but we are looking forward to it.”

The closest PSG came to a goal was when Zlatan Ibrahimovic fired into the net in the closing minutes but was narrowly ruled offside.

City goalkeeper Joe Hart said it was an amazing night.

“We have worked hard in this competition. We struggled to start with but we have started to compete.”

On Wednesday, titleholders Barcelona defend a 2-1 lead at Atletico Madrid, while Benfica host Bayern Munich, 1-0 down from the first leg. The semi-final draw will be made on Friday.