( CNN ) -- Borussia Dortmund moved a big step closer to a first German Bundesliga title in nine years on Saturday with a historic 3-1 victory over defending champions Bayern Munich at the Allianz Arena . Jurgen Klopp 's team moved 13 points clear of second-placed Bayer Leverkusen , who visit Werder Bremen on Sunday , and 16 ahead of Bayern -- who lost at home to Dortmund for the first time in 20 years . Louis van Gaal 's team dropped to fourth after the home defeat , occupying Germany 's final Champions League position for next season with 10 rounds to play . Paraguay striker Lucas Barrios opened the scoring in the ninth minute with his 11th goal of the season after Bayern midfielder Bastian Schweinsteiger lost posesssion to Kevin Grosskreutz , who threaded a perfect pass into the penalty area . Welcome win for struggling Wolfsburg . Brazilian defender Luis Gustavo equalized seven minutes later with his first goal for Bayern since arriving from Hoffenheim in January , sidefooting in a volley from Franck Ribery 's corner . Dortmund immediately went back in front through a wonderful effort from Turkey midfielder Nuri Sahin , who curled a 20-yard left-foot shot past goalkeeper Thomas Kraft . Bundesliga top scorer Mario Gomez thought he had leveled again in the 20th minute , but the striker was ruled to be offside . Former Bayern defender Mats Hummels sealed the Westphalian team 's victory with a header from Mario Gotze 's corner on the hour mark . With 15 minutes left , Dortmund 's 22-year-old Australian keeper Mitchell Langerak capped a solid Bundesliga debut when he denied Germany international Gomez from close range . Hanover claimed third place after central defender Christian Schulz 's last-gasp header was enough to see off St. Pauli . The 27-year-old converted from Portuguese winger Sergio Pinto 's 87th-minute corner to put Mirko Slomka 's team two points ahead of Bayern , . Mainz remained in fifth place after also needing a late goal to snatch all three points away to Hoffenheim . Former Austria midfielder Andreas Ivanschitz put the visitors in front before his compatriot David Alaba looked to have rescued a draw for ninth-placed Hoffenheim in the 84th minute . But with just four minutes left , 30-year-old Colombian midfielder Elkin Soto secured victory for Thomas Tuchel 's Mainz with his second league goal of the season . Germany international Lukas Podolski scored an 88th-minute winner to help Cologne beat SC Freiburg and climb into 11th position , eight points behind their opponents . Sixth-placed Hamburg could only manage a 1-1 draw away to relegation-threatened Kaiserslautern . Marco Kurz 's Kaiserslautern drew first blood through Adam Hlousek 's first-half goal , but Marcell Jansen 's leveler for Armin Veh 's Hamburg left the home team in 15th position and above the relegation play-off place on goal difference . Schalke 's disappointing Bundesliga season continued with a 1-1 draw at home to Nuremberg . Nuremberg , currently eighth in the table , took the lead through Jens Hegeler , only for former Real Madrid and Spain striker Raul to equalize after 52 minutes .
Borussia Dortmund record first win away to Bayern Munich since 1991 . The 3-1 victory leaves Jurgen Klopp 's team 13 points clear at the top of the table . Hanover move up to third above Bayern after a last-gasp 2-1 triumph at St. Pauli . Second-placed Bayer Leverkusen will travel to Werder Bremen on Sunday .