Bastian Schweinsteiger headed in a deft Toni Kroos chip to give Bayern the lead in the 40th minute before early second half goals from Thomas Muller and Kroos made sure the Bavarians bounced back in style from their first league defeat last week.
Bayern's ninth win in 10 league games lifted them to 27 points.
Hoffenheim's Sven Schipplock scored in injury time to condemn second-placed Schalke 04 to a 3-2 defeat that leaves them seven points adrift.
"It was a good goal and more importantly a crucial one," said Muller of his seventh goal of the season that helped Bayern clinch their first win in Hamburg in six years.
"Finally we won again here because it had been an issue for quite some time."
Bayern, hosting Lille in the Champions League on Wednesday, were eager to shrug off last week's defeat to Bayer Leverkusen and dispel any thoughts of a possible repeat of last season's mid-season implosion.
Hamburg, with three wins in their last four games, struggled to make an impact in Germany's traditional north-south derby.
It took only three minutes after the restart for Bayern to strike again with Muller's audacious shot from the tightest of angles beating Adler.
Kroos took any wind left out of Hamburg's sails drilling in from close range in the 53rd minute as Bayern set a Bundesliga record for five wins in five straight away games since the start of the season, without conceding a goal.
Dortmund were livelier from the start against Stuttgart and should have taken the lead midway through the first half when Mats Hummels' header was palmed onto the bar by Sven Ulreich and his rebound header was cleared off the line by Artur Boka.
