On the final German league weekend of 2013 before the winter break, Bayern were absent in Morocco preparing to take on Raja Casablanca in Marrakech in the FIFA Club World Cup final.
Leverkusen and Dortmund's defeats means Pep Guardiola's Bayern can go ten points clear if they beat Stuttgart in their catch-up fixture on 29 January.
Second-placed Leverkusen fell to a late goal at strugglers Werder Bremen, whose Argentinian right-back Santiago Garcia stabbed his shot home to give Bremen their first win in six games.
"It's a bit annoying that we go into the winter break on the back of two defeats," Leverkusen coach Sami Hyypia said after Bayer were shocked 1-0 by Eintracht Frankfurt last Sunday.
"We controlled the game, but we didn't score a goal and lacked a bit of belief.
"It leaves a bitter taste in the mouth, but all in all we can be happy with the first half of the season."
Borussia Dortmund's poor league form continued with a 2-1 defeat to Hertha Berlin, their third straight home defeat, which threatens to see them finish the weekend outside the automatic UEFA Champions League places.
Despite reaching the knockout stages in Europe as group winners, Dortmund have picked up just four points in their last six league games.
"We allowed our opponents to get back in the game and didn't take our chances in the second half," lamented Dortmund coach Jurgen Klopp.
"Hertha got brave and realised there was something to be had after the second goal, while we allowed ourselves to become too hectic."
Borussia took an early lead at home when captain Sebastian Kehl put through a superb ball for Marco Reus and with his first touch, the Germany winger put his shot past 18-year-old Hertha goalkeeper Marius Gersbeck, who was making his Bundesliga debut.
But Hertha got back on level terms when striker Adrian Ramos hit his 11th goal of the season after Hertha's Sami Allagui put in a cross for the Colombia forward to convert on 23 minutes.
Tunisia forward Allagui then gave Hertha the lead by pouncing on a mistake by Dortmund's teenaged centre-back Marian Sarr, rounding Dortmund goalkeeper Roman Weidenfeller and firing into an empty net on the stroke of half-time.
Klopp substituted the clearly distressed Sarr for the start of the second-half, moving left-back Kevin Grosskreutz into centre-back, but his side failed to grab a precious equaliser despite seven minutes of added time.
Dortmund stay third but will drop to fourth if Borussia Monchengladbach pick up at least a point at home to Wolfsburg on Sunday.
Nuremberg remain winless
Nuremberg finish 2013 as the only team in a major European league without a win so far this season after they were held to a goalless draw at home to Schalke.
The Royal Blues were without coach Jens Keller, who has been told a decision on his future will be made over the winter break, as the 43-year-old was suffering with flu.
Freiburg extended Hanover's appalling away record to eight consecutive defeats with a 2-1 win to help the hosts in their bid to escape the bottom three.
Japan striker Shinji Okazaki hit a late winner after Mainz had scored two goals in three minutes to bounce back from conceding an early goal for a 3-2 win at ten-man Hamburg.