Their performance was a warning to title favourites Bayern that any slip-up, such as their 3-1 defeat to Borussia Monchengladbach on Friday when the season restarted after a one-month winter break, would be costly.
Schalke are third, also on 37, taking full advantage of Bayern's lapse with their own 3-1 win over VfB Stuttgart on Saturday
"We had the chance to go up to 37 points today and we did exactly that," Dortmund coach Jurgen Klopp told reporters.
"Everything worked well but it was just one game. Now we move forward. The good thing is that we are ruthless in applying our game."
In the only other match on Sunday, Champions League competitors Bayer Leverkusen saw their two-goal lead evaporate in three minutes. Lars Bender's header in the 70th rescued a 3-2 win over Mainz 05 to lift them to 29 points in sixth place.
Borussia gave the hosts, whose nine-game unbeaten run come to a crashing end, no chance and dominated from the start with dazzling pace and Kevin Grosskreutz deservedly put them ahead in the 16th minute.
With Hamburg, who had not lost in the league since October 2, having to deal with a full-pitch pressing game and a shaky defence, it did not take long for the champions to strike again.
Lewandowski picked up the ball on the left, beat two defenders and chipped the ball over charging goalkeeper Jaroslav Drobny for a two-goal cushion in the 37th minute.
The champions picked up where they had left off after the break with Blaszczykowski thundering in a low drive on the hour after poor defending by the hosts.
The Poland international then converted a penalty 14 minutes from time before his countryman Lewandowski took advantage of yet another defensive blunder inside the box to fire in his 14th league goal of the season while thousands of Hamburg fans poured out of the stadium.
Paolo Guerrero scored a late consolation goal for Hamburg in the 86th.
The result lifted second-placed Dortmund to 37 points, with Bayern ahead on goal difference despite their defeat at fourth-placed Gladbach.
Hamburg, who could do nothing to avoid their first league defeat under coach Thorsten Fink, dropped to 14th and two points above the relegation zone.
"We delivered a bad game. We had far too much respect and I really do not know why," said Fink. "We lacked courage and this is something we will need to work on this week."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.