Ernesto Valverde's Bilbao team punished the visitors with clinical counter-attacks, playing with the advantage of having won the first leg 1-0 in Madrid.
IMAGES from Serie A matches played on Saturday.
The other semi-final will see an Italian side, Milan or Roma, come up against Bayer Leverkusen or West Ham.
IMAGES from football matches played across Europe on Wednesday.
Erling Haaland had the same points as Lionel Messi but lost out by having fewer first-place votes from national team captains.
A second-half goal by forward Lautaro Martinez earned Inter Milan a 1-0 victory over rivals AC Milan in their Champions League semi-final second leg.
Norwegian Haaland beat his team mate Kevin De Bruyne and 2022 World Cup champion Lionel Messi after helping City win three major trophies, the Champions League, English Premier League and FA Cup.
Indian Grandmaster D Gukesh scored a crushing victory over Alexander Donchenko in the 10th round of Tata Steel Masters in Wijk Aan Zee, Netherlands on Thursday.
Metz draw at Marseille to end losing streak
'OK. RM was not happy we were celebrating KDB goal,' Haaland, whose son has scored 51 goals for city in his first season in England, said on Twitter.
'It was a long career, really long, thank you to everyone who gave me the strength, the adrenaline and the emotion to continue.'
Holders Real Madrid will play 2021 winners Chelsea in the Champions League quarter-finals while Manchester City's Pep Guardiola will visit his former club Bayern Munich.
Manchester City face Inter Milan in the Champions League final in Istanbul on Saturday.
Now only Inter stand in the way of a treble that would match Manchester United's still unique feat of 1999.
La Liga leaders Real Madrid were held to a frustrating 1-1 draw at lowly city rivals Rayo Vallecano on Sunday as Joselu's early strike was cancelled out by Raul de Tomas' penalty, a result that could spice up the title race with surprise package Girona.
A summary of the UEFA Champions League Group Stage action, on Wednesday.
For Napoli, the match highlighted their struggling form, marking three consecutive defeats across all competitions for the first time since October 2016. They are fifth with 24 points.
Images from the Champions League Round of 16 matches.
Real Madrid midfielder Luka Modric came off the bench to net a stunning strike from the edge of the box late in the second half to secure a 1-0 home win over Sevilla on Sunday and stretch their lead at the top of La Liga to eight points.
Chelsea came from behind to beat Crystal Palace 3-1 thanks to added time goals from Conor Gallagher and Enzo Fernandez.
IMAGRS from the soccer matches played across European leagues on Friday
David De Gea has left Manchester United following the end of his contract after 12 seasons with the Old Trafford side.
La Liga leaders Real Madrid cruised to a 4-0 home win over relegation-threatened Celta Vigo on Sunday to restore their seven-point lead at the top of the table with a dominant display.
Manchester City marched into the Champions League final for the second time in three seasons after outclassing holders Real Madrid 4-0 for a 5-1 aggregate victory.
City fans were in dreamland after their side finally lifted the Champions League trophy
Atletico Madrid secured a hard-fought 2-1 home victory over Real Betis in La Liga on Sunday thanks to an own-goal by Rui Silva and a header by Alvaro Morata as Diego Simeone's side ended a three-game winless run in all competitions.
Round-up of football matches played around Europe on Saturday.
City completed the treble of Champions League, Premier League and FA Cup titles, matching Manchester United's feat in 1999 and drawing comparisons with Guardiola's 2008-09 Barcelona team.
Juventus climb to top of Serie A with win over Lecce
Erling Haaland became the third player in Champions League history to score five goals in a game as he led Manchester City to an unrelenting 7-0 rout of RB Leipzig in the second leg of their last-16 tie.
Tottenham Hotspur beat Nottingham Forest 2-0 away with goals by Richarlison and Dejan Kulusevski for a second straight win that nudged them closer to the Premier League top four on Friday although they had midfielder Yves Bissouma sent off late on.
Thunderstorm could not dampen the rousing victory parade as Manchester City celebrated completing the long-awaited treble.
News of all that transpired on and off the football field.
Atletico celebrate anniversary with 3-1 comeback win over Mallorca
Barcelona were drawn in Group E with Bayern Munich, Benfica and Dynamo Kyiv.
Yokohama beat Shandong to book Asian Champions League last 16 berth
Images from the UEFA Champions League group matches played on Tuesday night.
IMAGES from the football matches played across Europe on Sunday.
Players were in tears after Rodri's emphatic second-half goal against Inter Milan in the final secured a 1-0 victory
The first legs of the ties will take place on February 16, with the return match a week later on February 23.