Aged 35 years and 259 days, the former France international slotted in Bayern's opener midway through the first half before adding a second with a scuffed finish late on.
Saturday's performance could have been even more memorable for Ribery, had Robert Lewandowski not failed to control the veteran's pass at the culmination of a superb run.
Bayern's win was capped off in style in the 89th minute with Rafinha's fortuitous effort making it 3-0, which also brought up a record for coach Niko Kovac.
The Bundesliga champions have now won their last five league fixtures, and it is the first time Kovac – in his either his playing or managerial career – has claimed five successive wins in Germany's top division.
This recent spell of good form has also served to remove some of the pressure off the coach's back, following reports that his job might be on the line following a disastrous start to Bayern's Bundesliga defence.
Die Roten lost three of their first 11 league outings, including a 3-2 defeat at the hands of Borussia Dortmund that helped BVB set a commanding lead at the summit.
The victory means Bayern end 2018 six points behind leaders Dortmund, and three above third-place Borussia Monchengladbach.