Dortmund, which had a four-point lead, moved seven points clear of Bayern and stayed four clear of second-placed Borussia Moenchengladbach, which defeated Werder Bremen 3-1 away.
Brazilian-born midfielder Jorginho converted the spot-kick after substitute Federico Chiesa earned the late penalty for Italy.
Both teams were disappointing in their opening games. Colombia, down to 10 men, was upset 2-1 by Japan and Poland lost to Senegal by the same score in Group H.
Senegal are making their comeback to the World Cup after 2002, while Poland are in Russia after failing to qualify for the 2010 and 2014 editions.
Poland are preparing for their first World Cup appearance since 2006, meaning Lewandowski and Szczesny will be making their debuts.
Lewandowski has scored 106 goals in 126 Bundesliga games for Bayern since switching from league rival Borussia Dortmund in 2014. He helped the team win the league each year, chipping in 29 goals this season.
Bayern Munich end their season with the league title only as Frankfurt astonished the Bundesliga champions 3-1 to win the German Cup final at Berlin.
Lewandowski polished off the win with two late goals to give Bayern a seemingly insurmountable five-goal cushion ahead of the second leg of the last-16 tie in Istanbul on March 14.
Reus was handed the captain's armband 259 days after the German forward sustained a cruciate ligament injury in the German Cup final.
Bayern Munich won the DFL Supercup against arch rivals Borussia Dortmund in the Signal Iduna Park in a penalty shootout with star man Robert Lewandowski stepping up.
Munich: Bayern Munich striker Robert Lewandowski has regretted his decision to vote Real Madrid forward Cristiano Ronaldo in the Fifa Ballon d'Or ahead of teammate Manuel Neuer.The Poland skipper picked Ronaldo ahead of his Bayern
FRANKFURT, Germany : Borussia Dortmund beat Bayern Munich 2-0 in the German Super Cup on Wednesday to win the first domestic title of the season. Dortmund shut down former teammate Robert Lewandowski, while on the
PORTLAND, Oregon : Landon Donovan scored the winning goal as the Major League Soccer All-Stars came from behind to beat German champion Bayern Munich 2-1 on Wednesday. Donovan, who formerly played in Germany for Bayer
Berlin: Robert Lewandowski scored to give Borussia Dortmund a hard-fought 1-0 win over Werder Bremen on Friday and maintain the team's winning start to the Bundesliga.Lewandowski broke the deadlock in the 55th minute, when Marco
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