Costa, who joined from Shakhtar Donetsk in the close season for a reported 30 million euros (21 million pounds), has impressed at the Audi Cup with his speed and control on the left wing in the absence of regular wide players Arjen Robben and Franck Ribery, who are out injured.
"We are still in preparation but showed good signs. We need to keep working for the season start," Bayern sports director Matthias Sammer told reporters a week before the Bundesliga gets underway.
Real were missing the firepower of their regular attacking trio with Cristiano Ronaldo and Karim Benzema out injured and Gareth Bale on the bench.
Bayern had a handful of good chances and hit the post through Thomas Mueller in the first half.
Costa then set up Lewandowski with a superb cutback but the Pole somehow managed to fire wide in front of an empty goal.
Former Bayern player Toni Kroos had Real's best chance when he tested keeper Manuel Neuer with a powerful shot, but it was Bayern who looked the likelier to score.
The German champions, eyeing a record fourth straight Bundesliga title this season, did just that when Costa found Lewandowski with a pinpoint free kick for the only goal of the game in the 88th minute.
"Better to have the earlier miss before the league starts," Lewandowski said. "Now we will get ready for the German Cup (first round this week)."
Bayern, who beat AC Milan 3-0 on Tuesday, take on fifth-tier Noettingen on Sunday.
($1 = 0.9172 euros)
(Reporting by Karolos Grohmann; editing by Toby Davis)
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