The result could spell a premature end to their title hopes after 18 games although second-placed Mainz 05 and Bayer Leverkusen, also on 33 points in third spot, plunged to defeat.
"We are all very disappointed," said Bayern coach Louis van Gaal. "It should have been 3-0 at half-time for us but instead we made mistakes.
"You can't win if you make mistakes like that."
Bayern took a seventh-minute lead when Wolfsburg keeper Diego Benaglio raced out of the box and his attempted clearance hit Thomas Muller's leg before rolling into the net.
A sixth league goal of the season by Ruud van Nistelrooy, who is on Real Madrid coach Jose Mourinho's transfer wish-list, gave Hamburg SV a 1-0 victory at Schalke 04 that lifted them to seventh with 27 points.
It was supposed to be the start of Bayern's renewed battle for the championship, following the winter break, and the aggressive visitors were on course early on when Mario Gomez rattled the crossbar and then Mueller gave them the lead.
Wolfsburg fought back to win a penalty in the dying seconds of the first half but Bayern's new first choice keeper Thomas Kraft did well to palm Grafite's spot-kick on to the bar.
Robben's arrival added pace for Bayern who dominated the second half without converting any of their half-dozen chances and the Bavarians were punished when Riether levelled.
