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|Lewandowski (R) celebrates scoring in Bayern's resounding win over Hamburg on Saturday. (Photo: AFP/Guenter Schiffmann)|
The victory keeps Bayern on course to wrap up another Bundesliga title - their sixth in a row - before the end of March, and heaps misery on Hamburg, who are now without a win in 13 games.
"We played very well today. The performance and result were very important for us," said Bayern coach Jupp Heynckes, whose side go to Besiktas for the second leg of their Champions League last-16 tie in midweek, leading 5-0 from the first leg.
With eight games left, Bayern are a huge 20 points clear of second-placed Schalke, who won 1-0 at Mainz on Friday.
"It doesn't matter if we are 10, 15 or 20 points ahead, we need to keep going in the Bundesliga," said Arjen Robben. "We can't just focus on the Champions League."
Bayern have made a habit of recording big home wins over Hamburg at the Allianz Arena in recent years and it took them less than eight minutes to take the lead this time.
Franck Ribery broke away on the left before rounding goalkeeper Christian Mathenia to slot in the opener.
Just four minutes later, Lewandowski headed in a Joshua Kimmich cross to double the lead for Bayern. The Polish international struck again in the 19th minute, after a pinpoint long ball from Jerome Boateng had opened up the Hamburg defence.
Robben fired in Bayern's fourth on 55 minutes, and Ribery made it five with a mazy solo run in the 80th minute.
Lewandowski blasted one penalty over the bar on 85 minutes, before converting a second spot-kick at the death to complete his hat-trick.
His latest exploits in front of goal mean he has now scored 100 Bundesliga goals for Bayern and is the club's all-time leading foreign goal-scorer with 142 from 182 games in all competitions.
He overtakes the Brazilian Giovane Elber, who played for the club from 1997 to 2003.
Meanwhile, Hamburg remain seven points adrift of safety as they seek to avoid a first relegation in their history.
"The game was over after 18 minutes," Hamburg coach Bernd Hollerbach told Sky. "There is no shame in losing in Munich, but I am not happy with the way we lost."
Bayer Leverkusen move up to third after battling to a 2-0 victory over Borussia Moenchengladbach.
After an uneventful first half-hour, Lucas Alario put Leverkusen ahead in the 39th minute. Kevin Volland headed Leon Bailey's cross into the path of Alario, and the Argentinian swept the ball past goalkeeper Yann Sommer.
Josip Drmic missed a golden opportunity as Gladbach rallied late in the game, but Julian Brandt put the game beyond reach in stoppage time.
Defeat sees Gladbach slip behind Augsburg in the table, after Michael Gregoritsch fired them to a 3-1 away win over Hanover 96.
Gregoritsch fired Augsburg in front on 26 minutes, heading in a deep cross from Caiuby at the far post.
Salif Sane levelled the scores with a brilliant volley 10 minutes later, but Gojko Kacar headed Augsburg back in front on the stroke of half-time.
In the 83rd minute, an Augsburg counter-attack saw Gregoritsch secure victory for the away side.
Freiburg held Hertha Berlin to a 0-0 draw, while Bruno Labbadia is still without a win as Wolfsburg coach after watching his side lose 3-0 to Hoffenheim.
Nico Schulz gave Hoffenheim the lead on 19 minutes, sliding home a loose ball at the end of a smart passing move.
The home side continued to dominate and were rewarded with two goals in quick succession 10 minutes from time.
A well-angled strike from Serge Gnabry made it 2-0 on 77 minutes, before a calamitous Joshua Guilavogui own-goal secured victory.
Borussia Dortmund host Eintracht Frankfurt in the standout game on Sunday.
German Bundesliga results on Saturday:
Bayern Munich 6 Hamburg 0
Hoffenheim 3 Wolfsburg 0
Hertha Berlin 0 Freiburg 0
Hanover 96 1 Augsburg 3
Bayer Leverkusen 2 Borussia Moenchengladbach 0