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Griezmann scored his 31st goal of the season to send Atletico through

Atletico Madrid reached their second Champions League final in three years by edging past Bayern Munich on away goals in a pulsating semi-final.

Trailing 1-0 from the first leg in Spain, Bayern levelled the tie through Xabi Alonso's deflected free-kick.

Atletico keeper Jan Oblak saved Thomas Muller's low penalty, before Antoine Griezmann coolly fired in an equaliser.

Robert Lewandowski's header set up a tense finish, but Atletico held on after Fernando Torres missed a penalty.

Bayern, backed by a vociferous home crowd, desperately pressed for a third goal that would send them through.

However, they could not find a way past Oblak, who blocked David Alaba's 20-yard volley in injury time.

Atletico, aiming to be crowned European champions for the first time, will meet Manchester City or Real Madrid in the final in Milan on 28 May.

City face Atletico's neighbours at the Santiago Bernabeu on Wednesday after the teams drew 0-0 in last week's first leg.

Relive an eventful night in Munich

Football Daily: Bayern Munich v Atletico Madrid digital match report

Decisions, decisions, decisions...and drama

There was a tense atmosphere throughout the second leg in Munich, with the tie delicately balanced until the final whistle.

Bayern's opening goal, Muller's penalty miss and tempers flaring on the touchline - Pep Guardiola and Diego Simeone animatedly disagreeing over a decision - had already made for an entertaining first half.

Griezmann's vital away goal and Lewandowski's close-range finish - nodding in Arturo Vidal's headed cross from four yards - pointed towards even more drama in the final 15 minutes.

However, the anticipated Bayern onslaught failed to materialise.

Instead, Atletico won a penalty, despite Torres being fouled outside the box, before Simeone lost his cool again when he appeared to strike a member of his own staff.

Still Bayern needed only one goal to progress - and had five minutes of added time to score it. But Atletico survived, sparking wild celebrations among Simeone and his players.

Bayern had less average possession in the final 15 minutes than they did over the full 90, while they managed just two more shots on target after Lewandowski's goal

Third time lucky for Atletico?

Atletico have lost twice in the final of Europe's leading club competition - to Bayern in the 1974 European Cup and against neighbours Real two years ago.

Against a team playing in their fifth successive semi-final, they produced another display of remarkable defiance at the Allianz Arena.

German champions Bayern had 33 attempts on goal and 72% of possession - but it still was not enough to beat the gritty Spaniards.

The hallmark of Atletico's recent success has been their strength in defence, with Simeone's side developing a reputation as one of the toughest teams in Europe to break down.

However, the quality of their clinical attack should not be overlooked.

Atletico had not even managed a single touch in the Bayern penalty area until Griezmann fired in from the edge of the box.

The France striker marginally beat the Bayern offside trap, latching on to Torres' through ball before coolly drilling underneath Bayern keeper Manuel Neuer.

More Spanish misery for Pep

Guardiola is regarded as one of the world's greatest coaches, having won trophies galore with both Barcelona and Bayern Munich.

But the Spaniard will leave for Manchester City in the summer having failed to deliver the Champions League in his three-year spell in Bavaria.

Guardiola had acknowledged that winning the club's sixth European crown - or not - would be how his reign at Bayern was judged.

His side lost against Spanish opposition in the semi-finals in each of the past two seasons - to Real Madrid in 2014 and his former club Barcelona last year.

Atletico were well placed to make it an unwanted hat-trick after Saul Niguez's sublime first-leg goal in Madrid put them in control.

Bayern's first-half dominance was illustrated by the average position graphics of both teams. Virtually all of the home men (left) played in the Atletico half, while the visitors (right) were penned back in their own territory

The Spanish title hopefuls rode their luck at times after Alonso's opener, particularly in the first half when they were outclassed by an aggressive and high-pressing Bayern side.

But they regrouped after the break, keeping their discipline and shape as Bayern's 12th successive Champions League home win proved meaningless.

"We tried to press them high, have counter-attacks and this was why we got the goal," said former Liverpool and Chelsea striker Torres.

Not Muller time

Muller was named in the Bayern starting line-up after he was surprisingly left on the bench in Madrid last week.

Guardiola was heavily criticised in the German media for that decision, with Muller - who has scored 32 goals in 46 matches this season - so often a match-winner for club and country.

But the Germany forward's most decisive contribution in the second leg was failing to convert his first-half spot-kick.

That would have put Bayern ahead in the tie for the first time, just as Atletico's usually unruffled defence started to look rattled.

"The missed penalty gave us life," said Atletico coach Simeone, who was close to tears after Griezmann's goal.

Man of the match - Jan Oblak

Atletico keeper Oblak made nine saves in Munich, most crucially from Muller's penalty

The stats you need to know

Atletico Madrid progressed to the final after their 100th tie in Europe's leading club competition.

Antoine Griezmann is Atletico Madrid's top scorer in Champions League history with nine goals.

Thomas Muller has missed his past two penalties in the Champions League, scoring seven out of 10 in the competition.

Jan Oblak has saved two of the three penalties he has faced as Atletico Madrid's keeper (all competitions).

All six of Xabi Alonso's goals for Bayern have been scored from outside the box.

Alonso's goal was the first Atleti had conceded in 632 minutes in any competition.

Only Cristiano Ronaldo (10) has more goals in the Champions League semi-finals than Robert Lewandowski (six).

Pep Guardiola has been knocked out in his past four Champions League semi-finals.

What next?

Before Atletico can turn their attention to the Champions League final, they must focus on a thrilling Spanish title race.

Simeone's second-placed side, who won La Liga in 2014, are level on points with defending champions Barcelona with two games left. Third-placed Real Madrid are a point further behind.

Bayern, meanwhile, can still win the domestic double in Guardiola's final season in charge.

Two more points will clinch their fourth straight Bundesliga title even if nearest rivals Borussia Dortmund win both of their final two games.

They face Dortmund in the German Cup final on 21 May.