With a dazzling performance that will act as a warning to Italy's Juventus ahead of their Champions League quarter-final next week, Bayern, resting several key players, could have celebrated their 23rd German league title were it not for Borussia Dortmund's Robert Lewandowski.
The Poland striker scored a late winner earlier on Saturday to give the champions a narrow 2-1 victory at VfB Stuttgart and put Bayern's title champagne on ice for at least another week.
With a 20-point lead over second-placed Dortmund, however, the Bavarians look set to lift their 22nd Bundesliga trophy.
"We played textbook football at times today and the title cannot really slip away any more," Bayern coach Jupp Heynckes told reporters.
"It was important to fill up on confidence. But Tuesday's game will be different with Juve being a top European team and much more aggressive."
For Hamburg it equalled their heaviest defeat in the Bundesliga's 50 years and put a dent in their hopes of claiming a European spot.
"I have not experienced this as a coach before," said Hamburg's coach, Thorsten Fink. "I do not have an explanation for this 9-2. Everyone has to be self-critical, both team and coach."
Bayern, looking for a treble of titles this season, unleashed one attack after another from the start, with Xherdan Shaqiri opening their account with a low drive in the fifth minute.
Bastian Schweinsteiger headed in their second goal before Pizarro volleyed in from close range and Robben added another in a scintillating 33-minute spell.
Peruvian Pizarro, the Bundesliga's all-time top foreign scorer, got his second goal on the stroke of half-time and completed his hat-trick eight minutes after the restart with a superb backheel before Dutchman Robben was again on target a minute later.
"We are in great form and we played very well," Pizarro told reporters. "We have almost secured one trophy but we want three. That is what we showed out there today."
Third-placed Bayer Leverkusen kept on course for the Champions League with a 4-1 win over Fortuna Dusseldorf. Two goals apiece from Stefan Kiessling and Andre Schuerrle left them four points behind Dortmund on 48.
Schalke 04 leapfrogged into fourth place after leaving it late to beat relegation-threatened Hoffenheim 3-0 with three goals in the final 19 minutes.
Freiburg also improved their European chances, easing past rivals Borussia Monchengladbach 2-0 to move into seventh place on 39.
Max Kruse, linked with a move to Gladbach next season, struck twice in Freiburg's first win in five matches.
In Stuttgart, early substitute Lukasz Piszczek headed a Marco Reus free-kick past goalkeeper Sven Ulreich for Borussia Dortmund's opener in the 29th minute.
Stuttgart worked their way back into the game and Alexandru Maxim drew them level with a low drive in t
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