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Rodrigo Tello netted the only goal for the Turkish side after 20 minutes with a shot from distance.
United have already qualified for the knockout stage but they still need a point from their visit to Wolfsburg, who lost 2-1 to CSKA Moscow, in a fortnight to claim top spot.
"I think we were a bit anxious but its not a bad thing - they're young and you expect that," said United manager Alex Ferguson, who fielded a largely young side for the match.
"It was a stellar performance in terms of the flow of the game and we've shown some really good things," added Ferguson.
Bayern Munich, facing an early Champions League exit, revived their chances of reaching the last 16 as they beat Maccabi Haifa 1-0 and rivals Juventus lost at Girondins Bordeaux, who have qualified for the knockout stage.
Bayern will in the next round face Juventus, who collected eight points, one clear of third-placed Bayern.
Haifa, bottom of the group, have yet to score a point or a goalin the competition.
"I saw a very good match against a very tough team," Bayern coach Louis van Gaal told reporters. "It could have been more than just one goal. I think it was one of our best games.
"I think now the chances are 50-50 against Juventus," he said. "We will get our chances in Turin."
In Group C, nine-time champions Real Madrid took a huge step towards securing their place in the last 16 with a 1-0 victory over FC Zurich.
AC Milan failed to keep pace with Real in the same group as they were held 1-1 by Marseille, leaving both qualifying spots wide open in Group C.
In Group D, Chelsea ensured they would finish top with an efficient 1-0 win away at Porto. Both teams have qualified for th eround of last 16.