Wolfsburg were cruising towards a point before Bulgaria striker Dimitar Rangelov headed Cottbus ahead in the 72nd minute and the hosts proved the goal was no fluke when Albania midfielder Ervin Skela added a second on 86 minutes.
The valuable three points takes Cottbus out of the bottom three while Wolfsburg missed the chance to go five points clear and suffered their first league defeat since they lost 2-1 at Werder Bremen in December.
"We wasted some big chances and therefore we lost the game," said Wolfsburg coach Felix Magath. "Our forwards did not have their best day and when you don't take your chances, you won't win. We were not as strong and compact as we would have liked to be. For us it is about taking fifth place and getting into Europe next season, so things look good."
The result is even more extraordinary as Cottbus were hammered 4-0 at Schalke in their last league game - a defeat so bad they offered their travelling fans a refund on their match tickets.
Despite the shock upset, Wolfsburg stay two points clear at the top of the table with Hertha Berlin second after midfielder Patrick Ebert hit a first-half goal to seal a 1-0 win at early-season pacesetters Hoffenheim on Friday.
The leaders' defeat means three of the top five sides - Bayern Munich, Wolfsburg and Hamburg - all lost this weekend while Hertha and Stuttgart seized their chance, with three points now separating the top five.
Bayern's 1-0 loss at home to Schalke on Saturday leaves the defending champions in third place, while Hamburg's 2-0 defeat at Borussia Dortmund puts Martin Jol's side back in fifth.
With five matches remaining, Hamburg are on 54 points with both Stuttgart and Bayern, with Hertha Berlin on 55 and Wolfsburg leading with 57.
In Munich, Schalke grabbed a first-half winning goal through Turkey striker Halil Altintop before the Royal Blues had midfielder Jermaine Jones sent off for a second yellow card on 70 minutes to earn the consequential red.
Bayern then lost French midfielder Franck Ribery when he was shown a second yellow card on 76 minutes.
Dortmund have won five league games on the trot and are up to seventh in the table after their win over Hamburg.
Hamburg went behind when the ball was played in from the left and midfielder Sebastian Kehl shot past Hamburg goalkeeper Frank Rost after 32 minutes, with Swiss striker Alexander Frei then converting a 90th-minute penalty.
Stuttgart are fourth in the table after strikers Cacau and Mario Gomez scored in the 2-0 win over Eintracht Frankfurt which keeps them in the five-way title race.
Werder Bremen came from 2-0 down to beat Bochum 3-2 thanks to goals from striker Hugo Almeida, Brazil defender Naldo and midfielder Diego, leaving them 10th as they prepare for Thursday's UEFA Cup clash with Hamburg.
Bottom side Karlsruhe gave themselves a chance of staying up after beating Bayer Leverkusen 1-0 with one of the luckiest goals of the season.
Karlsruhe defender Sebastian Langkamp lunged at the ball on the halfway line to try to win possession, but got more than he could have dreamed of when the ball curled over the Leverkusen defence and goalkeeper Rene Adler and into the net.
His 72nd-minute strike leaves Karlsruhe two points behind relegation rivals Borussia Mönchengladbach, who drew 1-1 with Bielefeld on Sunday, while mid-table Hanover enjoyed a 2-0 win over Cologne on Saturday.