AC Milan missed a chance to qualify with a game to spare when they were held 1-1 by Olympique Marseille while Real Madrid put one foot in the second round by beating FC Zurich 1-0 with a pedestrian performance on Cristiano Ronaldo's return from injury.
Manchester United, already through to the second round, lost a 23-match unbeaten home record in the tournament as they were beaten 1-0 by Turkey's Besiktas at Old Trafford -- one of only 12 goals in eight games on an uninspiring night of football.
With no additions to the list of teams already qualified -- Girondins Bordeaux, Olympique Lyon, Arsenal, Manchester United, Chelsea, Porto, Fiorentina and Sevilla -- eight more places will be at stake in the final round of matches next month.
Bayern's fate was largely out of their hands as they kicked off knowing that a win for Juventus against already qualified Bordeaux would send the Italians through.
Facing a team who had not scored a point or goal, Bayern did their part when Croatia's Ivica Olic tapped in the winner from a rebound in the 62nd minute for their only goal in three home group games.
Bordeaux did Louis van Gaal's team a favour when Brazilian Fernando and Moroccan Marouane Chamakh scored in the second half to give them a 2-0 win over Juventus. Bayern, who have seven points from five games, stayed third in Group A but moved within one of Juventus. The Bavarians must beat Juventus in their final game to qualify at the Italians' expense.
Group C continued on its unpredictable way when unsung Argentina forward Gonzalo Higuain's first-half goal against the Swiss champions sent Real top with 10 points.
It was all they could manage despite facing a defence which had conceded 12 goals in their previous four group games.
Real were booed off although there was a cheer when Ronaldo replaced Raul in the second half to end a two-month injury layoff.
Real moved two points ahead of AC Milan who, needing a win to qualify against Marseille, went ahead with a 10th minute goal by Marco Boriello but gifted Lucho Gonzalez an equaliser six minutes later.
Marseille are a further point behind but need to beat Real by four goals in their last match to qualify.
Milan's last game is away to the Swiss side, who beat them 1-0 at the San Siro earlier in the group. German champions VfL Wolfsburg missed a chance to book their place when they lost 2-1 at CSKA Moscow, who revived their own hopes in Group B. Both teams have seven points.
Previously winless Besiktas produced the evening's big shock when Chilean Rodrigo Tello's long-range shot in the 20th minute handed Manchester United their first home defeat in the competition since their 2005 loss to AC Milan.
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