Goals by Germany striker Miroslav Klose and Ribery, plus a late penalty from Lukas Podolski, gave Bayern their fourth straight league win in the Bundesliga.
The victory puts the defending champions third on 21 points, but Hoffenheim reclaimed the top place they lost for 24 hours with a 4-1 win over Karlsruhe to lead the table with 25 points.
“I am contented that we took three points and have improved our place in the table,” said Bayern coach Jurgen Klinsmann. “We had to have patience against a very organised Bielefeld side and we had to work hard.”
Having endured criticism from Bayern manager Uli Hoeness after two poor games, Podolski’s improved performance was especially pleasing for Klinsmann.
“Lukas Podolski showed exactly the reaction which I have expected from him,” he said.
Bayern took the lead at Munich’s Allianz Arena when Ribery whipped in a free-kick which was saved, but when the ball fell to Klose he slipped his marker and slotted home his shot on 25 minutes.
But Bielefeld were level just five minutes later when Bayern defender Martin Demichelis, who scored an own goal against Frankfurt on Wednesday, gave away a penalty and Poland striker Artur Wichniarek rifled home the spot kick.
Munich had Bielefeld under immense pressure in the second-half as they created 11 shots in just over 20 minutes early on, including a header from defender Lucio which hammered the crossbar.
Having squandered a bucket load of chances, Bayern finally got the deserved break through on 77 minutes when Podolski fed a pass into Ribery who slid his shot home.
And Podolski smashed home a penalty on 84 minutes as the home side dominated.
Bielefeld lost midfielder Robert Tesche on 82 minutes when he hacked down Ribery through sheer frustration and was shown a straight red card.
Having lost top place in the league for less than 24 hours to Bayer Leverkusen, Hoffenheim went back to the summit with a win over Karlsruhe.
After a slow start, Hoffenheim striker Vedad Ibisevic netted twice and is the league’s top scorer with 13 goals in 11 games, while Nigeria striker Chinedu Obasi also scored two goals.
“I do not think that we started that well and we only really made amends after a quarter of an hour,” said Hoffenheim coach Ralf Rangnick. “The reaction of the team when we went 1-1 was very good, we are of course very happy to get a big win.”
Werder Bremen picked up their first league win since the end of September when they raced into a 3-0 half-time lead against Hertha Berlin and eventually won 5-1.
Title-contenders Hamburg suffered a shock when they went down 3-0 at Hanover, having been 2-0 down after just 18 minutes, and VfB Stuttgart were also humbled 3-1 at home to strugglers Cologne.
But Schalke 04 managed a late 2-0 win over second-from-bottom Energie Cottbus thanks to a second-half goal from Germany defender Heiko Westermann on 80 minutes and a penalty from Peru striker Jefferson Farfan on 90 minutes. Bayer Leverkusen briefly led the top of the table following Friday night’s convincing 2-0 win at home to Wolfsburg after a second-half strike from midfielder Tranquillo Barnetta and a header from striker Stefan Kiessling.
Mid-table Borussia Dortmund are home to strugglers Bochum on Sunday while bottom side Moenchengladbach host Eintracht Frankurt.