Bayern, who take on Valencia in the Champions League on Wednesday, were without wingers Franck Ribery and Arjen Robben, out of the squad with minor injuries.
Coach Jupp Heynckes again left €40 million signing Javi Martinez on the bench at the start.
Bayern striker Claudio Pizarro came on late in the game to equal the record for most Bundesliga matches by a foreign player at 336 but it was Toni Kroos who made sure of the three points when he struck in stoppage time from a fine Martinez pass.
Dortmund had no such case of nerves and a well-timed Mats Hummels header put the champions on track to maintain their 12-month unbeaten run at home. They also extended their league run to 31 games without defeat, closing in on the all-time record of 36 matches set by Hamburg.
Jakub Blaszczykowski fired in another goal from the far post six minutes before the break against a toothless Leverkusen side before fellow Pole Robert Lewandowski headed in another in the 78th to lift second-placed Dortmund to seven points from three games, two behind leaders Bayern.
In an exciting derby Hanover confirmed they were the top team in the north with a last-gasp 3-2 win over Werder Bremen to move into second place and seven points but with a better goal difference than Dortmund.
Szabolocs Huszti scored twice for Hanover including a superb stoppage-time bicycle kick to hand his team their second win in three games but the Hungarian was then promptly sent off with a second booking during celebrations.
Borussia Moenchengladbach lost 3-2 to Nuremberg after a bad start to the game saw them having to crawl back from two goals down. Luuk de Jong got one back and Granit Xhaka equalised in the 53rd minute, only for the outstanding Hiroshi Kiyotake to swiftly put Nuremberg ahead again.
Stuttgart managed secured their first point and pulled themselves off the bottom with a goalless draw against Fortuna Duesseldorf.
Former US secretary of State Henry Kissinger kept his promise to attend a home game of Greuther Fuerth, his childhood club before immigrating to the United States, when he took his seat for the 2-0 defeat to Schalke.
Kissinger, a Nobel Peace Prize winner, was born in Fuerth in 1923 but his Jewish family left Nazi Germany in 1938. He had promised years ago he would watch a home game from the stands if they won promotion to the Bundesliga.
"I wish them now the championship title," said the 89-year-old former top diplomat before kick-off, donning a green-and-white scarf and wearing a dark blue suit. "I am happy to be able watch a first division game after a long time."
He said he always got into trouble for watching games at the Ronhof stadium as a child instead of going to the opera as his father suggested.
Club boss Helmut Hack called him "our best known ambassador globally".
"It is great that he kept his promise," he said.