Suspensions to Thomas Muller and Robert Lewandowski saw Bayern starting without their attacking talisman, as the visiting side missed Alassane Plea.
Monchengladbach were on the back foot ten minutes from kickoff, as Marcus Thuram pulled up injured with a twisted knee and was replaced by Breel Embolo.
A chance immediately presented the league leaders an opportunity to go ahead, but Mickael Cuisance couldn't make the most of Ivan Perisic's inch-perfect layoff.
Yann Sommer had to come to Gladbach's rescue at the midway stage with a sprawling save from a right-footed strike by Lucas Hernandez.
Sommer didn't cover himself in glory four minutes later after poor possession and positioning saw Joshua Zirkzee take full advantage to bag the opener for the home side.
Gladbach were back level on 37 minutes as misfortune from Benjamin Pavard found the Frenchman slipping Patrick Herrmann's ball into his own net.
The second half started with a change from the visiting outfit, who introduced Tony Jantschke for Nico Elvedi.
Gladbach threatened to go ahead afterwards with Stefan Lainer's 25-yard strike skimming the top of the crossbar, as Bayern shot-stopper Manuel Neuer pulled off his first save to deny Herrmann.
The Bavarians regrouped and almost regained the lead in the final quarter as a stunning volley from Serge Gnabry brought the best out of Sommer.
Bayern's persistence resulted in the visitors finally succumbing after Leon Goretzka got goal-side to turn home Pavard's telling ball four minutes from time.
A response from Gladbach almost materialised in the remaining minutes, but Bayern worked tirelessly to preserve their lead and regain their seven point lead at the top. They only need one more win to secure the title.