Bayern Munich snapped its own shutout streak 1 draw against Napoli on Tuesday in the Champions League.
Bayern last allowed a goal on the opening day of the Bundesliga season on Aug. 7, and Toni Kroos scored inside 2 minutes at the Stadio San Paolo to lift his side into an early lead.
But Badstuber turned Edinson Cavani's cross past goalkeeper Manuel Neuer late in first half, snapping an 1,146-minute shutout streak for Bayern.
Mario Gomez had a penalty kick saved early in the second half by Napoli goalie Morgan De Sanctis, as the Italians managed a point without a shot on goal.
Bayern still sits atop Group A with seven points from three matches, as it won at Villarreal and at home against Manchester City in its first two games.
Napoli extended its home unbeaten streak to 10 matches in European play and is second with five points. Napoli tied at City, and beat Villarreal at home.
Bayern and Napoli meet again Nov. 2 in Munich, as every match from Tuesday and Wednesday will be replayed in the next round at the opposite site.
Manchester City 2, Villarreal 1
Manchester, England - Sergio Aguero scored in stoppage time as English Premier League leader Manchester City earned an important win, 2-1 over Villarreal on Tuesday at Etihad Stadium in Group A of the Champions League.
City had just a point from its first two matches, a draw against Napoli and a loss against Bayern Munich, and Villarreal moved in front after 4 minutes when Cani scored.
An own goal from Carlos Marchena tied the fixture just before half, and Aguero found the net 3 minutes into stoppage time when he directed the match-winner into the net at the left post from just a few steps off the line.
City remained within three points of Bayern for first in the group and climbed to within just one point of Napoli, while Villarreal has lost all three games and sits bottom without a point.
Inter Milan 1, Lille 0
Inter was stunned by Trabzonspor in its group opener, but Pazzini helped the Italians post their second successive win to take command of the group after three matches.
Lille is the lone winless team in the group, but it still has two points from draws in its first two matches, and is just two points out of second place.
CSKA Moscow 3, Trabzonspor 0
Moscow, Russia - Seydou Doumbia scored twice, and CSKA Moscow rolled to a 3-0 win over Trabzonspor on Tuesday at Luzhniki Stadium in Champions League Group B play.
Doumbia has four goals through three group matches, helping CSKA Moscow total four points. He scored in the 29th and 86th minutes, with the latter a cheeky chip-shot from inside the area. Aleksandrs Cauna also scored for CSKA.
Trabzonspor, which stunned Inter Milan in its first group match, lost for the first time but also sits on four points from three matches.
Manchester United 2, Otelul 0
Bucharest, Romania - Wayne Rooney converted two second-half penalties to help Manchester United escape Romania with a 2-0 victory over a tough Otelul at the Stadionul National in Group C of the Champions League.
Otelul kept the match scoreless through 65 minutes, but a foolish handball by captain Sergiu Costin set up the first penalty, which Rooney converted to the right.
Nemanja Vidic was shown a red card just a minute later for United, but Patrice Evra drilled the right post in the final minutes and Rooney was fouled in the area in stoppage time to set up his second penalty.
United won for the first time in three Champions League matches and climbed to second in the group, two points behind Benfica. Otelul has lost all three of its games.
Benfica 2, Basel 0
Cesar scored in the 20th minutes and Cardozo clinched the Portuguese club's second win in the 75th. Benfica leads the group by two points over Manchester United, while Basel is three points back in third.
Basel won its opener over Otelul, then tied United 3-3 at Old Trafford, but is facing trips to Benfica and Otelul, and a rematch with United in Switzerland.
Real Madrid 4, Lyon 0
Madrid, Spain - Karim Benzema's 19th-minute goal against his old club sparked Real Madrid to a 4-0 win over Lyon on Tuesday at the Bernabeu in Group D play in the Champions League.
Sami Khedira and Sergio Ramos added goals in the second half, when an own goal accounted for the third strike. Real remained perfect through three matches in Group D, outscoring its opponents 8-0 to take a commanding lead.
Lyon sits on four points from three matches, level on points with Ajax for the second spot and a berth in the knockout round. Ajax currently holds second via a tiebreaker.
Ajax 2, Dinamo Zagreb 0
Zagreb, Croatia - Derk Boerrigter and Christian Eriksen scored as Ajax earned a 2-0 road win over Dinamo Zagreb on Tuesday at the Stadion Maksimir to climb into second place in Group D of the Champions League.
Boerrigter broke the deadlock four minutes after halftime, and Eriksen scored in the 90th to seal three points for Ajax. The Dutch side is even with Lyon on four points, but holds the edge on a tiebreaker.
Dinamo Zagreb has lost all three of its matches.