Matthias Ginter had an early chance for Freiburg with a header from the middle of the box that when just over.
The away side threatened to take the lead through Rafael van der Vaart, but his shot from outside the area was palmed away.
With 20 minutes gone Francis Coquelin squandered another chance for the home side, heading over from around seven yards out.
The poor finishing continued as this time Pierre-Michel Lasogga hammered a shot wide.
It was 1-0, however, to Hamburg shortly before half time when Maximilian Beister drilled in a right-footed shot from the edge of the box.
Bert van Marwijk's team added two goals in the second half, one through Lasogga and the other from Van der Vaart's left boot.