The win kept Bayern five points clear at the top as they again inflicted on their opponents their heaviest league defeat.
The Pole, who has netted 19 times in the Bundesliga this season, struck twice in the first half and slotted in his third goal in the 54th minute after Arturo Vidal had put the hosts ahead in the 17th.
Strugglers Hamburg had been confident they would not be the punch bags of past matches between the sides, having also lost 8-0 in Munich two years ago, and they had been unbeaten in their last three games.
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But they looked shell-shocked as they conceded another goal by David Alaba in the 56th and substitute Kingsley Coman scored twice more within five minutes a little later.
Arjen Robben struck on the break as Hamburg again capitulated to the Bundesliga champions and current leaders.
"A perfect day, a perfect game," said Ancelotti. "The team played an outstanding game and I could not be happier."
"I told my players before the game that I wanted a good match for my anniversary. I never thought it would be that good. I hope we show the same attitude in our next game."
Bayern never gave Hamburg a chance, making amends for their last-gasp 1-1 draw at Hertha Berlin last week.
They had 75 percent possession in the first half alone and could have added to their tally with Lewandowski also hitting the woodwork.
"I think we did not win a single one-on-one throughout the entire first half," Hamburg keeper Rene Adler said. "It's just intolerable."
Second-placed RB Leipzig stayed five points off the pace after beating Cologne 3-1 to climb up to 48 points.
Pierre-Emerick Aubameyang ended his goal drought after 471 minutes to score twice as Borussia Dortmund tightened their hold on third place with a 3-0 victory at Freiburg.
Dortmund are on 40 points, three ahead of Hoffenheim who play Schalke 04 on Sunday.
Hertha Berlin beat 10-man Eintracht Frankfurt 2-0 with goals from Vedad Ibisevic and Vladimir Darida in the second half to leapfrog their opponents into fifth place.
Eintracht, two points behind in sixth, had Haris Seferovic sent off for elbowing an opponent.
(Reporting by Karolos Grohmann, editing by Ed Osmond, Clare Fallon and Neville Dalton)
