In other matches, VfL Wolfsburg edged past Hertha Berlin 2-0; promoted Ingolstadt snatched a last-gasp 1-0 win at Werder Bremen
Bayern Munich's French teenager Kingsley Coman scored his first Bundesliga goal in their 3-0 victory over promoted Darmstadt 98 on Saturday as the German champions went three points clear at the top of the table with their fifth straight win.
The 19-year-old Coman, who joined on a two-year loan deal from Juventus this season, drilled in from a perfect Sebastian Rode cutback for a 2-0 lead as Bayern rested several players after their 3-0 Champions League win at Olympiakos this week and ahead of a big midweek Bundesliga game against VfL Wolfsburg.
Earlier, a scintillating run by winger Douglas Costa drew three players to the Brazilian who laid it off for Arturo Vidal to drill home off the post for his own first goal for the Bavarians in the 20th minute.
Rode, making a rare start this season in a crowded Bayern midfield, netted Bayern's third goal on the rebound after his first effort bounced off the post following another through ball from Costa to make sure of Darmstadt's first loss this season.
"I am very satisfied. We interpreted the game very well and did not allow anything at the back," Bayern coach Pep Guardiola told reporters.
"I know what it means to play here after the Champions League."
The Bavarians, who saw Javier Martinez make his first appearance of the season after a five-month injury break, are on a maximum 15 points from their opening five games, three ahead of Borussia Dortmund, who host Bayer Leverkusen on Sunday.
"I am very happy for Javi because I have missed him this year," said the Spaniard.
VfL Wolfsburg edged past Hertha Berlin 2-0, but left it late with two goals from substitute Bas Dost, including an 88th minute penalty, securing a deserved victory.
The Wolves, who also beat CSKA Moscow in midweek to make a winning start in the Champions League, are in third place on 11 points and have extended their unbeaten run to 25 matches.
Fellow Champions League club Borussia Moenchengladbach slumped to a 1-0 defeat at Cologne for their fifth straight defeat.
Gladbach, who finished third last season, have yet to earn a point this season, and are languishing in last place after their worst ever Bundesliga start.
Promoted Ingolstadt snatched a last-gasp 1-0 win at Werder Bremen with a stoppage-time penalty to move up to fifth on 10 and become the first league newcomer to win their first three away games.
Hamburg drew 0-0 against Eintracht Frankfurt but moved up to tenth on seven points.