Goals from Roberto Firmino, Niklas Sule and Andreas Beck secured victory for the hosts which eased their relegation fears and and left their opponents in the bottom three.
The emphatic win also saw Hoffenheim rid themselves of the Bundesliga's worst defensive record.
That now belongs to Hamburg, who have conceded 43 goals. Their record of being the only club in German football never relegated from the Bundesliga is now looking under serious threat.
Hoffenheim, who narrowly beat the drop last season, seemed to show a little more appetite for the fight compared to an increasingly nervous-looking Hamburg, and they took the lead through Firmino after a quick counter-attack.
Sule took full advantage of some poor Hamburg defending to head the hosts two in front before the break.
Hoffenheim goalkeeper Koen Casteels remained untested, meanwhile, as Hamburg showed no ideas going forward and glaring lapses in concentration at the back.
Another of those was punished again by Firmino, who dribbled his way round the back and sent a low ball in for Beck to make it three and increase the pressure on Hamburg coach Bert van Marwijk, whose side still did not show any signs of a reaction.
Should Nurnberg get the better of Hertha Berlin on Sunday, Hamburg will drop into the automatic relegation places.