Mario Mandzukic and Bastian Schweinsteiger scored inside 13 minutes and Toni Kroos added a late goal as Bayern Munich won 3-1 over Mainz on Saturday to continue its perfect start in the Bundesliga.

Mandzukic, the lone striker with Mario Gomez out injured, notched his third of the season in the second minute and Schweinsteiger followed with his second in just three matches in the 13th minute at the Allianz Arena.

Kroos added a stoppage time goal, as Bayern erased any doubt about the outcome and secured sole possession of first place for another week. Bayern has three wins from as many games and has outscored its opponents, 12-2.

Adam Szalai converted a second-half penalty kick for Mainz, which lost for the second time against one draw this season.

Mandzukic received a pass from Thomas Muller and scored to the bottom left for the opening goal, and Holger Badstuber delivered a cross that Schweinsteiger headed into the bottom right as Bayern took a quick two-goal lead.

Mainz found its way back into the match after half when Bayern defender Dante gave away a penalty, and Szalai converted to the bottom left just before the hour mark to pull a goal back for the visitors.

Bayern maintained its one-goal cushion with the help of Javi Martinez, who was pulled off the bench in the second half to make his second appearance off the bench since arriving from Athletic Bilbao for a league-record $50 million.

Martinez also provided the final assist of the match, setting up Kroos for his second goal of the new season.

Bayern, which was also without Franck Ribery and Arjen Robben, opens Champions League play Wednesday against Valencia in Munich.

Borussia Dortmund 3, Bayer Leverkusen 0

Dortmund, Germany - Jakub Blaszczykowski scored his second goal of the season, and Borussia Dortmund bounced back from a draw in Nurnberg with a 3-0 win over Bayer Leverkusen on Saturday at Signal Iduna Park.

The two-time defending Bundesliga champions were held to a 1-1 tie in Nurnberg before the international break, but Mats Hummels opened the scoring before the half-hour and Blaszczykowski added a second six minutes before halftime.

Robert Lewandowski capped the scoring 12 minutes from time as Dortmund notched its second win against the draw to remain two points off the pace of three-win Bayern Munich.

Dortmund opens Champions League play Tuesday against Ajax at home, as it tries to escape the "Group of Death," which also includes Real Madrid and Manchester City.

Leverkusen lost for the second time against one win through three matches.

Hannover 3, Werder Bremen 2

Hannover, Germany - Szabolcs Huszti scored his second goal of the match in the third minute of stoppage time as Hannover beat Werder Bremen, 3-2, on Saturday at AWD-Arena in the Bundesliga.

Huszti and Leon Andreasen scored inside 10 minutes as Hannover jumped out to a two-goal lead, but Bremen responded through goals from Aaron Hunt off the spot in the 24th minute and Kevin De Bruyne in the 74th.

Huszti rescued all three points for Hannover with just seconds remaining as he deposited a cross from Konstantin Rausch from 12 yards. Huszti was sent off after the goal, as he received a second yellow for celebration.

Hannover won its second straight to remain unbeaten, and sits second and just two points off the pace of three-win Bayern Munich.

Bremen lost for the second time through three games, and is six points off the pace already.

Nurnberg 3, Monchengladbach 2

Monchengladbach, Germany - Hiroshi Kiyotake scored the match-winner 10 minutes into the second half as Nurnberg defeated Monchengladbach, 3-2, on Saturday at Borussia Park to remain unbeaten in the Bundesliga.

Timm Klose and Timmy Simons scored eight minutes apart in the opening half as Nurnberg grabbed a two-goal lead inside 25 minutes, but Gladbach answered with goals from Luuk de Jong and Granit Xhaka on each side of halftime.

Kiyotake responded two minutes after Nurnberg saw its lead evaporate as he was able to deposit a pass from Hanno Balitsch with a shot from the edge of the area to the bottom-left corner in the 55th minute.

Nurnberg has a maximum six points from its two road matches, as it opened with a 1-0 win in Hamburg. Nurnberg tied Borussia Dortmund, 1-1, in its lone home match, and is just two points off the pace of three-win Bayern Munich.

Monchengladbach dropped its first match of the season, and sits on four points from three games.

Stuttgart 0, Dusseldorf 0

Stuttgart, Germany - Dusseldorf earned a 0-0 tie against Stuttgart at Mercedes Benz Arena to maintain its perfect defensive record and extend its undefeated start in the Bundesliga.

Newly-promoted Dusseldorf returned to the Bundesliga with a 2-0 road win at Augsburg and tied Monchengladbach, 0-0, in its second league match. Dusseldorf has five points from three matches, and is four points off the pace of three- win Bayern Munich.

Stuttgart secured its first point after losses to Wolfsburg and Bayern to open the season.

Schalke 2, Greuther Furth 0

Furth, Germany - Julian Draxler and Lewis Holtby scored as Schalke warmed up for its Champions League opener against Olympiacos with a 2-0 win at Greuther Furth on Saturday at Trolli Arena in the Bundesliga.

Schalke visits the Greek club Tuesday to open Group B play and stayed unbeaten in Germany with its second win against a draw from three matches ahead of the key European match.

Draxler opened the scoring three minutes after halftime and Holtby notched his second goal of the new campaign two minutes from time as Schalke sealed its second straight win.

Promoted Greuther Furth lost its second through three weeks. Furth dropped its opener against Bayern Munich and beat Mainz in its second match.