Leverkusen are looking to become only the third club after Hoffenheim and Borussia Moenchengladbach to beat Bayern in the league this season.
Leon Bailey hit the bar for Leverkusen moments before Franck Ribery cut in from the left and slammed home his first league goal of the season.
League top-scorer Robert Lewandowski and Germany defender Mats Hummels are fit after overcoming knocks, and Heynckes can call on a full squad apart from long-term absentees Manuel Neuer and Thiago Alcantara.More news: Donald Trump says he would 'beat Oprah' in presidency battle
However, the goal sparked Leverkusen into life.
Heynckes was the last Bayern coach to win at Friday's opponents Bayer Leverkusen, but that was in his previous spell in charge back in 2013.
However, Rodriguez sealed the win for the Bundesliga leaders in stoppage time with a lovely free-kick that found the top corner to make it 3-1 to the Bavarians.
"Mark Uth is now the best German goal scorer in the Bundesliga and will really improve our attacking options from the summer", said Schalke sporting director Christian Heidel.More news: Scientists find thick sheets of ice just below Mars' surface
"It's a game which has all the ingredients that make football so attractive; both teams can play good football and it's going to be tough", he said.
"If there is a need for discussion, we all sit down and decide what is best, while also keeping other alternatives open".
Wagner's career has come full circle after spells at Werder Bremen, Kaiserslautern, Hertha Berlin, Darmstadt and most recently Hoffenheim, winning his first cap for Germany past year and has scored five goals in seven appearances for his country. Leverkusen definitely don't want to start falling to the wrong end of that crowd, and a shocking win over Bayern would not only help them start to gain separation from the pack, it would help them gain some much-needed momentum to keep pulling away.
The 46-year-old later said he was ashamed of his actions after dramatically tumbling to the ground after faint contact with Gladbach's Denis Zakaria in the technical area.More news: Buy tickets - Tickets - The North American Bitcoin Conference