The 35-year-old Frenchman tapped in his first goal in the 35th minute and added another in the 79th to take his tally to four goals in four league matches, with club bosses recently saying this was his last season at Bayern.
The Bavarians, who had half a dozen injured absentees, including Arjen Robben, James Rodriguez, Serge Gnabry and Mats Hummels, added a third goal with Rafinha in the 89th and are now on 36 points following their fifth straight league win.
Leaders Dortmund are top on 42 after beating Borussia Moenchengladbach, in third on 33, 2-1 on Friday. After Sunday's matches the season will resume on Jan. 18.
"We had a tough time earlier in the season but now you can see that we have improved a lot," Ribery told reporters. Bayern, who have won the last six league titles, had dropped to sixth a few weeks ago after a dip in form.
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"I am very happy for my team. I have been here 12 years and that has always been the case. I work hard and will try to keep playing like that and then we will see what will happen next season."
Ribery has not confirmed he will be leaving at the end of the season and has hinted recently that he may try to stay on.
Frankfurt enjoyed a strong start with Bayern keeper Manuel Neuer coming to the rescue on several occasions before his Frankfurt counterpart Kevin Trapp made three superb saves to deny David Alaba, Javi Martinez and Thomas Mueller.
But Trapp was beaten when Mueller and Robert Lewandowski combined superbly outside the box to set up Ribery for the lead.
Mueller came close to a second goal a minute before the break but his header bounced off the crossbar.
Bayern tried to slow down the game but Frankfurt kept at it and Danny Da Costa should have levelled for the hosts from two metres out but instead fluffed his back-heel effort.
Ribery, however, played a fine one-two with Lewandowski a little later and despite mis-hitting his shot the ball went in off the post.
Another miskick from Rafinha sent the ball high over Trapp and into the net as Bayern sealed their win in Frankfurt with a lucky third goal and ended the Bundesliga year on a high.
(Reporting by Karolos Grohmann; editing by Clare Fallon)
