Record nine-time champion Madrid will host the return match in the two-game series on April 30, with Bayern visiting Barcelona the following night.
The winners will meet in the May 25 final at Wembley Stadium in London. German teams have never met in the title match of Europe’s elite club competition.
“It was only the first leg, but we can still be very satisfied with the result,” Lewandowski said on the website of tournament organizer UEFA. “But we still only took the first step tonight and we haven’t reached the final yet.”
Lewandowski scored in the eighth minute before Cristiano Ronaldo tied the game just before halftime with his competition- best 12th goal. Lewandowski scored twice more in the opening 10 minutes after the break and added his fourth goal from the penalty spot later in the half.
The victory matches Dortmund’s biggest in the Champions League. The 1997 European Cup winner remains the only unbeaten team in this year’s competition and has won all six of its home matches by a combined score of 14-4.
“The best team by far won,” Real coach Jose Mourinho said on UEFA’s website. “Individually and collectively Dortmund were better and deserved their victory.”
Real Madrid will have to match the biggest comeback in Champions League history to avoid a third-straight semifinal loss. Deportivo La Coruna lost its opening quarterfinal 4-1 at AC Milan in 2004 before winning the second leg 4-0 at home.
“It will be very difficult in the return leg at home but we must remain confident,” Real captain Sergio Ramos said on UEFA’s website. “When the draw for the semifinals was made a lot of people thought this was going to be easy for us but this is a German team we are talking about. They are a great side.”
The teams met in this season’s group stage with Dortmund winning 2-1 at home in October and drawing 2-2 in Spain in November en route to finishing atop the group.
Dortmund’s Marco Reus forced a one-handed save from Diego Lopez in the seventh minute, with Lewandowski unable to get to the rebound in front of the open net. Lewandowski scored a minute later as he got away from Real defender Pepe to slide and direct in Mario Goetze’s cross from the left.
Madrid’s first shot came in the 24th minute as Ronaldo’s long free kick was parried away by goalkeeper Roman Weidenfeller.
Dortmund had a claim for a penalty kick denied by referee Bjorn Kuipers as Reus went down in the area after coming together with Raphael Varane. The decision drew the ire of the home fans and less than a minute later Real was even.
A back pass from Mats Hummels was intercepted by Gonzalo Higuain, who took off down the right before sliding a pass for Ronaldo to put into the open net. It was Ronaldo’s 50th Champions League goal, making him the fifth player to reach the milestone.
Dortmund regained the lead five minutes into the second half as Reus passed to Lewandowski, who turned and put a shot past Lopez. The Real players appealed for offside and television replays showed the striker held his line as he took the pass.
Lewandowski completed his hat trick five minutes later by firing a shot into the roof of the net from close range. He’s the first player to score three goals against Real Madrid in a European Cup match.
Lewandowski completed the scoring from the penalty spot in the 66th minute after Xabi Alonso took down Reus in the area. It was his 10th goal of the competition, putting him second in the scoring chart behind Ronaldo.
“It was a royal evening for us,” Dortmund midfielder Ilkay Gundogan said. “We played a great game from the start until the final whistle and deserved to win by this margin.”
To contact the reporter on this story: Bob Bensch in London at email@example.com.