A goal from Franck Ribery and a penalty by Austria international David Alaba put the Bavarians on 30 points. Schalke 04 are second after overcoming Werder Bremen 2-1 while Eintracht, without a win in three games, occupy third spot on 20.
Champions Borussia Dortmund eased past bottom club Augsburg 3-1, Robert Lewandowski netting twice and Marco Reus whipping in a curling free-kick from the tightest of angles to lift them up to fourth on 19 points.
Eintracht weathered an early storm as Bayern pushed forward in numbers, buoyed by their 6-1 midweek demolition of Lille in the Champions League.
"You cannot always win 6-1 and play great," coach Jupp Heynckes told reporters. "It was a hard-earned win against a good team.
"It is sometimes difficult to switch over from Champions League mode. At the end of the day we used our cleverness and our experience to win this one."
Bayern and Eintracht both set Bundesliga records earlier in the season.
The Bavarians won their opening eight games to chalk up the best start in the competition's 50-year history while Eintracht made the best start by a promoted side by winning five of their first six matches.
RIBERY GOAL
Frenchman Ribery, in dazzling form this season, missed a good chance early on when keeper Kevin Trapp got a foot to his low shot from seven metres.
Trapp twice more denied the winger before Eintracht started to cause the home defence a few problems.
The visitors, however, could do nothing a minute before the break when Javi Martinez found Ribery who scored with an easy tap-in.
Bayern lacked the explosive pace they possessed against Lille but were hardly threatened in the second half and Alaba converted a 77th-minute penalty to secure victory.
Schalke needed almost an hour to strike against Werder who took a 16th-minute lead when captain Aaron Hunt netted from a tight angle.
The visitors could have made it 2-0 when Sokratis Papastathopoulos headed against the bar but Roman Neustadter, fresh from receiving his first Germany call-up on Friday, levelled in the 59th minute.
Werder, the subject of media speculation suggesting that sports director Klaus Allofs could be joining VfL Wolfsburg, conceded another in the 69th minute when Julian Draxler fired in a Jermaine Jones cross to end their three-game unbeaten run.
Hamburg SV, who had Paul Scharner sent off for a second booking in the 35th minute, held on for a 0-0 draw at Freiburg while Fortuna Dusseldorf and Hoffenheim shared the points in a 1-1 draw.
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