Solskjaer took full advantage of the chance that fell his way.
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Former Real youth player Joselu pulled a goal back for Alaves in the 59th minute, powering in a header from a free kick, but Benzema rounded off the victory for second-placed Real with an exquisite solo run and goal in the 70th minute.
Manchester City marched into the quarter-finals of the Champions League
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The 25-year-old striker, who stands 1.76 metres tall, caught the eye on the big stage against Germany, driving home a penalty at the end of the first half before poking in the ball on 72 minutes following a rare blunder by Germany goalkeeper Manuel Neuer.
Didier Deschamps has let his hair go grey naturally since the last time he picked up a European title 16 years ago. The diminutive Deschamps was never a spectacular player -- a la Zinedine Zidane -- and certainly does not belong to the Jose Mourinho school of coaching with sensational sound bites. But the unglamorous Frenchman with the twangy voice has been instrumental in taking the host nation through to Sunday's Euro 2016 final against Portugal.
Real Madrid reached their 14th European Cup final and crushed Manchester City's hopes of a maiden title after Gareth Bale's deflected effort secured a 1-0 victory in the second leg of their Champions League last four clash on Wednesday.
A round-up of Saturday's football action in La Liga, Bundesliga and Ligue 1.
News of all that transpired on and off the football field.
The former Paris St Germain manager will be presented on Wednesday and will replace Jose Mourinho who left at the end of last season to join Chelsea.
Images from Saturday's action in La Liga.
A sloppy Real Madrid were held 0-0 at home to Real Betis on Saturday in a further blow to their hopes of retaining the La Liga title.
A summary of sports events and sports persons, who made news on Saturday
Germany midfielder Toni Kroos has eased Real Madrid's injury concerns and could be fit to play in their Champions League match at Borussia Dortmund on Tuesday, coach Zinedine Zidane said.
An insatiable Lionel Messi hit a hat-trick as Barcelona hammered Espanyol 5-0 in a local derby on Saturday to make it three wins from three and take full advantage after Liga champions Real Madrid were held to a 1-1 draw at home to Levante.
Karim Benzema fired Real Madrid to a 1-0 win in the city derby against Atletico Madrid on Saturday which underlined Real's La Liga title credentials. Bayern Munich scored three goals in the opening 26 minutes to defeat Mainz 05 3-1 away on Saturday and go two points clear at the top of the Bundesliga with their sixth straight win.
Real Madrid forward Vinicius Jr. score twice as his side punished a sloppy Liverpool to win 3-1, while Manchester City beat Borussia Dortmund 2-1 in Tuesday's Champions League quarter-final first leg.
In other European football action Real Madrid were left frustrated after a goalless draw against Athletic Bilbao in their La Liga match on Sunday.
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Images from Europa and Champions League matches played on Wednesday.
Real Madrid dropped points for the third time in seven games since Zinedine Zidane's return as they were held to a 0-0 draw away to Getafe in La Liga on Thursday, which harmed their neighbours' hopes of a top-four finish.
Barcelona defender Gerard Pique has decried the fans who booed manager Luis Enrique and the players in Sunday's laboured 2-1 home win over Leganes in La Liga as having a short-term memory.
Real Madrid's teenage Brazilian duo Vinicius Junior and Rodrygo Goes sent them top of La Liga as both scored in a 2-0 win over Osasuna on Wednesday.
Real Madrid's stuttering season continued as they were reduced to 10 men and then slumped to an 11th La Liga defeat of the campaign by going down 3-1 at Real Sociedad.
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Real Madrid's La Liga title bid took a dent after Zinedine Zidane's leaders were held to a 2-2 draw at home to Celta Vigo on Sunday, denied all three points by a late strike from Santi Mina. Lazio mounted a superb second-half comeback at the Olympic Stadium to beat Inter Milan 2-1 and move above Antonio Conte's side into second place in Serie A on Sunday.
With the year sprinting to a close, we bring you, in pictures, some of the best action from the sports world.
France midfielder Paul Pogba has rejoined Manchester United from Italian champions Juventus on a five-year contract, with the option to extend for a further year, the Premier League club said in a statement on Monday.
Summary of all that transpired on and off the football field
If history ultimately judges the finest talents by their achievements on the international stage, where neither player has tasted success, then the Portuguese captain could use Sunday's Euro 2016 final to land a haymaker blow in one of football's great rivalries.
10 Awesome Tips for Men for Using Trimmers
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A red hot Luis Suarez scored four goals and contributed three assists as Barcelona's stuttering La Liga title charge sparked back to life with a spectacular 8-0 thrashing of Deportivo La Coruna on Wednesday.
Barcelona must appreciate matching the club's record of nine wins and a draw in their first 10 games of a Liga campaign, especially after Real Madrid's defeat at Girona, coach Ernesto Valverde told a news conference on Monday.
Arsenal extend Aubameyang stay with new three-year deal
It looks like Emmanuel Macron just got lucky again.
On Saturday he made the difference yet again with two goals to help Real Madrid secure a third Champions League title in four years as they crushed Juventus 4-1 in a riveting final.
A round-up of Saturday's action in La Liga, Ligue 1 and Serie A.
Tite was asked about reports that he was set to take charge of the Champions League winners during a news conference ahead of Sunday's friendly against Austria, although it was not clear where they had originated.