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.
The defeat broke Leverkusen's 14-match unbeaten run in all competitions, dating back to the end of September, but the hosts stay fourth in the table.
"Tactically and defensively my team did it well for long stretches", coach Jupp Heynckes told reporters. The champions re-signed their former youth striker from Hoffenheim this summer.
Goalkeeper Sven Ulreich, who will again deputise for the injured Manuel Neuer, added: "They're risky opponents who break forward quickly".
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.
The Bavarians kicked off 2018 with a potential banana skin but demonstrated their class as goals from Javi Martinez, Franck Ribery and James Rodriguez saw them overcome a side who had not lost in their previous 12 Bundesliga games.
Bayern nullified the attacking threat of Leverkusen's dynamic trio of Julian Brandt, Leon Bailey and Kevin Volland - which was key to their success on the night.
Just when the hosts were on the front foot, Bayern doubled the scores out of the blue as Rodriguez passed into the path of Franck Ribery, who had all time and space to place the ball into the bottom near corner in the 59th minute.
He dribbled his way through the defence then unleashed a thunderbolt of a shot which gave Leverkusen's Germany goalkeeper Bernd Leno no chance.
Lewandowski, the Bundesliga's top-scorer with 15 goals in 17 games so far, is labouring with a knee injury while Hummels has a groin strain and the away match at Leverkusen's BayArena has come too early.