Defender Mats Hummels gave Dortmund an early lead but they were left fuming when Petar Sliskovic equalised from close range in the 89th minute with Dortmund's Neven Subotic down injured in the box with the referee allowing play to go on.
"This is a fair result in a way," said Dortmund coach Jurgen Klopp. "Mainz were a tough opponent and for us a lot went wrong today. We missed a penalty and then had to take (striker Lucas) Barrios off."
Ribery fired in a low left-footed drive to break the hosts' gutsy resistance and lift the champions to 48 points, two behind Hanover 96 who beat Hoffenheim 2-0.
Germany international Hummels' glancing header after eight minutes put Dortmund in the driving seat but Nuri Sahin failed to add another goal from the penalty spot minutes later when Wetklo did well to save his kick.
Freiburg could have levelled after 14 minutes but Papiss Demba Cisse saw his penalty saved by Thomas Kraft. The league's second highest scorer made amends three minutes later with his 18th goal, chesting the ball down to fire home from five metres.
"We were lucky not to be trailing after the first half," said Bayern coach Louis van Gaal. "Then we did play better and could get this win with a bit of luck through Franck Ribery's goal.
Michael Oenning's debut on the Hamburg SV bench was a success as his team crushed Cologne 6-2 with a hat-trick from Mladen Petric.
