Berlin: Luiz Gustavo scored in stoppage time to give Bayern Munich a 1-0 win at VfL Wolfsburg on Saturday, their first goal and points of the Bundesliga season, while champions Borussia Dortmund lost 1-0 at Hoffenheim.
Dutchman Klaas Jan Huntelaar hit a hat-trick as Schalke 04 came from behind to demolish hapless Cologne 5-1.
Mainz 05, who beat Freiburg 2-1 away, and Hanover 96, who won by the same score at Nuremburg, have six points from their opening two games.
Hamburg SV and promoted Hertha Berlin drew 2-2, allowing both sides to pick up their first point.
There were important, controversial refereeing decisions in three games, including Bayern`s where Wolfsburg had a goal harshly disallowed for offside.
Bayern, who suffered a shock 1-0 home defeat by Borussia Moenchengladbach in last week`s opener, were without Dutch winger Arjen Robben, who suffered a minor back problem in training on Friday.
Bayern striker Ivica Olic came on as a second-half substitute to make his first appearance for nine months following a knee operation and 19-year-old Japanese Takashi Usami made his Bundesliga debut, also after halftime.
Wolfsburg should have gone ahead when Patrick Helmes headed in from close range just after the half hour.
His effort was disallowed although replays showed he was clearly onside when a cross was played in.
Wolfsburg coach Felix Magath, whose side won 3-0 at Cologne last week, was livid at the decision and was still ranting when Bayern midfielder Toni Kroos was booked for diving in the penalty area shortly afterwards.
The game was heading for a draw until Croatian striker Olic escaped his marker on the left, found an unmarked Franck Ribery in the penalty area and the Frenchman laid the ball off for Luiz Gustavo to nonchalantly sidefoot home.
Dortmund, who began with an impressive 3-1 win over Hamburg a week ago, were beaten by an early Sejad Salihovic free kick at Hoffenheim.
The visitors had a penalty turned down when Shinji Kagawa appeared to be tripped just before the interval.
Schalke`s goal spree began with what looked to be an extremely harsh penalty awarded for handball.
It was converted by Huntelaar three minutes before halftime to wipe out Lukas Podolski`s early strike for Cologne.
Huntelaar and Lewis Holtby scored twice in as many minutes shortly after the restart, both goals set up by Marco Hoeger, and former Real Madrid and Spain forward Raul fired the fourth just before the hour.
Huntelaar completed his hat-trick six minutes from time as Schalke bounced back from last week`s 3-0 defeat at VfB Stuttgart.