Long-time leaders Dortmund had opened the door for Niko Kovac's side after suffering a shock 2-1 defeat to Augsburg on Friday and the reigning champions never looked in danger of failing to take advantage as they swatted aside their hosts, who now sit fourth.
Javi Martinez gave them a second-minute lead before Thomas Muller's fifth league goal of the campaign extended their lead nine minutes later.
Lars Stindl pulled one back for the hosts in the 37th minute, but Robert Lewandowski's glorious finish shortly after the restart extinguished any hopes of a comeback as Bayern – who added two more late on through Serge Gnabry and a Lewandowski penalty – cruised to an 11th win in their last 12 Bundesliga games.
Bayern started in devastating fashion, taking the lead inside two minutes.
Lewandowski's low strike was tipped around the post by Yann Sommer after just 30 seconds, but from the resulting corner Martinez headed into the roof of the net for his second league goal of the campaign.
Bayern's superb start got even better after 11 minutes, Muller turning in from close range after Sommer had kept out his initial effort.
The Monchengladbach goalkeeper then denied Lewandowski and Gnabry before Stindl clawed the hosts back into it eight minutes before the interval, the captain fizzing past Manuel Neuer from 15 yards.
Bayern started the second period in similar fashion to the first and restored their two-goal advantage in the 47th minute, Lewandowski collecting Thiago Alcantara's pass, swivelling superbly and clipping a fine finish past Sommer.
Gnabry added a fourth from close range in the 75th minute and Lewandowski scored from the spot in stoppage time after Joshua Kimmich had been tripped in the area to add gloss to a scoreline that sends an emphatic message to their title rivals, who now lead only on goal difference.
Momentum with Kovac's men
It has been a challenging first season in charge of Bayern for Kovac, but they are now surely favourites to claim a seventh Bundesliga title in a row. They look in irresistible form, while the wheels appear to be well and truly falling off for Dortmund – Lucien Favre's side have won just once in their last five games.
Lewandowski makes amends in style
The Polish striker was twice denied by Sommer in the first half – chances he would have expected to bury – but bounced back with a stunning strike early in the second half. His late penalty means he is now level on 195 goals with Claudio Pizarro as the Bundesliga's all-time top foreign scorer.
