The winger, who also became the Frenchman with the most German top-flight appearances, broke the deadlock early in the second half as Bayern maintained their perfect home league record this season.
Leverkusen were left to rue their failure to capitalise on a promising first-half showing, when they blunted the hosts' prolific attack and wasted two excellent early openings.
Ribery's strike changed the game entirely as Bayern grew in stature after the break, threatening to double their advantage on several occasions.
But one goal proved enough for Pep Guardiola's side to restore their seven-point lead at the summit.
The visitors were denied a surprise lead inside the opening three minutes when a defensive mix-up allowed Karim Bellarabi through to clip a shot over Manuel Neuer, but Juan Bernat did brilliantly to slide in and divert the ball away just before it crossed the line.
Roger Schmidt's side spurned another presentable opportunity in the seventh minute as Son Heung-min's delivery flashed across the face of goal, narrowly eluding the reach of Stefan Kiessling.
Despite dominating possession, Bayern offered little threat in the final third, with Robert Lewandowski restricted to a peripheral role by a well-marshalled Leverkusen defence.
Indeed, Schmidt's biggest concern in the first half was the sight of Kiessling going down injured following an innocuous challenge with Rafinha, although the Leverkusen stalwart did return after treatment.
The only other notable moment for Bayern before the interval was Arjen Robben's disallowed goal, the Dutchman half-volleying into the net after the whistle had gone for a foul on goalkeeper Bernd Leno.
And yet it took just six minutes of the second half for the champions to break the deadlock as Ribery volleyed home a left-footed strike from inside the box to ease the air of frustration around the Allianz Arena.
That foreshadowed a spell of concerted Bayern pressure, with Robben's attempted cross hitting the post after clipping Leno's right leg, while Lewandowski somehow found the side-netting after his own cross had been diverted back to him in front of an unguarded net.
Leverkusen showed commendable resolve to stay in the contest and managed to mount a few late attacks of their own, though Hakan Calhanoglu's wasteful free-kick summed up their lack of precision in the final third.
Bayern ultimately saw out the remainder of the game with relative comfort to seal a 10th consecutive home Bundesliga win, with tempers briefly flaring in the closing stages following Bellarabi's lunging challenge on substitute Sebastian Rode.
