The away victory - Bayern's first at Leverkusen since 2013 - leaves them 14 points clear and on course for a sixth straight Bundesliga title as the German league resumed after the winter break.
In the same breath, the many-time German champions will be keeping a close eye on explosive Leverkusen's Jamaican winger Leon Bailey, who has made a name for himself in the first half of the season with six goals and four assists.
However, Rodriguez sealed the win for the Bundesliga leaders in stoppage time with a attractive free-kick that found the top corner to make it 3-1 to the Bavarians.
Up next for Bayern is a home game against Werder Bremen, and it would not come as a surprise to see Munich continue their good run of form.
Both Ribery and Bayern's other veteran winger Arjen Robben, 34, are out of contract in June and the pair hope to be offered extensions in the coming weeks.More news: Everything President Trump has tweeted (and what it was about)
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"I have five months left and there are always many options", said Ribery.
Likewise, Bayern are trying to talk Heynckes into staying on as head coach past the end of the season. Borussia Dortmund, in third also on 28 points, host VfL Wolfsburg on Sunday.
Germany forward Thomas Mueller said Bayern are back at their best after struggling with fatigue through the final weeks of past year, even if results did not show it.
Heynckes said: "Joshua Kimmich will travel with the team, but I have to think about if he will start".
Only Manuel Neuer and Thiago Alcantara, both long-term injury absentees, will be missing for their trip to Leverkusen though Heynckes will have new signing Sandro Wagner available, with the forward having joined from Hoffenheim.
The 30-year-old Wagner, who made his global debut ahead of the Confederations Cup in Russian Federation, could well feature at Leverkusen. It's hard to win in Leverkusen.