First-half goals by Bayern's Chile and Brazil internationals gave Carlo Ancelotti's Munich a first win over Gladbach
Bayern Munich broke their Borussia Mönchengladbach jinx on Saturday as Arturo Vidal and Douglas Costa netted in a 2-0 home win to put the champions three points clear on Saturday.
First-half goals by Bayern's Chile and Brazil internationals gave Carlo Ancelotti's Munich a first win over Gladbach in five German league matches after Borussia claimed home and away league victories in 2015.
After back-to-back draws in the league the win caps a good week for Bayern, who enjoyed a 4-1 romp against PSV Eindhoven in the Champions League on Wednesday.
"The first half was perhaps our best of the whole season," said Ancelotti.
"The second wasn't quite so good and I told the players to be careful at the break as the energy wasn't 100 percent after the PSV game.
"They learnt the lesson from last weekend's draw with Frankfurt."
Ancelotti rested Germany forward Thomas Mueller from the starting line-up, but after Robert Lewandowski hit the post early on, Bayern went ahead after 16 minutes when Chile's Vidal headed home Rafinha's cross.
Winger Costa's 31st-minute shot doubled the lead at Munich's Allianz Arena, while Gladbach's best chance came when winger Andre Hahn hit the post on 71 minutes.
Hertha Berlin went second with a 2-1 home win over Cologne, who lost their unbeaten record.
Hertha took the lead in the capital when Mitchell Weiser broke clear and his pass found Vedad Ibisevic, who netted his sixth goal in eight league games on 13 minutes.
Cologne's French striker Anthony Modeste, the league's top scorer, levelled with his eighth goal in eight games on 65 minutes, but Hertha defender Niklas Stark headed the winner six minutes from time.
7Cologne's Simon Zoller hit the post in the dying stages, then replacement Artjoms Rudnevs had a goal disallowed and the result leaves their side fourth.
Borussia Dortmund are three Bundesliga games without a win, although they fought back from two goals down to draw 3-3 at Ingolstadt and sit sixth.
Dortmund were 2-0 down as Israel international Almog Cohen and Paraguay's Dario Lezcano netted for Ingolstadt.
Cohen wriggled free of his marker from a free-kick before Lezcano looped his header into the top corner.
Borussia hit back when Mario Goetze set up Pierre-Emerick Aubameyang to head home his seventh goal in his seven league games on 59 minutes, only for Lezcano to net Ingolstadt's third less than 60 seconds later to make it 3-1.
Dortmund dominated the final quarter as Adrian Ramos pulled a goal back on 69 minutes and Christian Pulisic scored the crucial equaliser in stoppage time.
The draw saw Ingolstadt climb off the bottom above Hamburg, who lost 3-0 to Eintracht Frankfurt on Friday.
Bayer Leverkusen slumped to a 3-0 defeat at home to Hoffenheim after playing virtually the entire match with 10 men.
Kevin Volland earned the fastest red card of the season with just six minutes gone for bringing down Kerem Demirbay, who was through on goal.
Demirbay, Sandro Wagner and Swiss midfielder Steven Zuber netted the visitors' goals.
Bayer coach Roger Schmidt was sent to the stands in the wake of the second goal and faces a lengthy ban for his second dismissal this year.
Ten-man Wolfsburg dropped to 15th after their 3-1 defeat at Darmstadt left them seven games without a win.
Frenchman Valerien Ismael was appointed Wolfsburg's new head coach on Monday after Dieter Hecking was sacked.
Freiburg were 2-1 winners at home to Augsburg as they claimed a fourth victory in as many matches in front of their own fans.