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Bayern, chasing a 12th straight league crown, were nowhere to be seen and managed only a single shot on target over the 90 minutes.
Xabi Alonso's team, who also twice hit the woodwork, are now on 55 points, with Bayern in second place on 50.
"Today it was a very disciplined performance from my team," said Alonso. "It was not easy but we waited for our chances. Maybe we did not have the ball too much today but we wanted to be dominant even without the ball."
"It was a very important win but it is just three points," he said. "We have to keep going. It is still February and we need to remain calm."
The game started with an eight-minute delay after fans threw candy onto the pitch before the start to protest the league's plan to let a financial investor take a stake in the Bundesliga media rights company.
Once proceedings got underway, the hosts proved more aggressive than Bayern, who initially had possession but lacked attacking ideas. The Bavarians were also shaky at the back, struggling with Leverkusen's increasing pressure.
They were caught napping when Robert Andrich, from a quickly taken throw-in, sent a cutback through the box with Stanisic, on loan from Bayern, left completely unmarked at the far post to tap in.
Spain international Grimaldo doubled the lead five minutes after the restart with his eighth league goal of the season before also hitting the crossbar with a wickedly curled corner kick.
The hosts gradually eased off but still came close to a third with Frimpong's low drive flying wide in the 73rd.
The Bavarians had no way back into the game, and even the league's top scorer Harry Kane failed to make any impact.
"We started well but then errors started creeping in," said Bayern coach Thomas Tuchel, whose team travels to face Lazio in the Champions League round of 16 next week.
"We were not able to carve out any chances, even later in the game when we had five or six attacking players. I don't have an explanation for why we did not get Harry more involved in the game."
