Jonathan Schmid's second-half goal was enough for Christian Streich's men to take all three points away from the HSV-Arena and move up to fifth in the table, above Eintracht Frankfurt on goal difference.
Hamburg are now four points adrift of the top six after their third consecutive defeat, and looking unlikely to challenge for a place in the Europa League.
Freiburg carved out two early chances, but were twice frustrated by the uprights as both Jan Rosenthal and Matthias Ginter hit the post with quick-fire efforts.
Rosenthal then squandered another good chance as the visitors gave as good as they got at the HSV-Arena.
Heung-Min Son led Hamburg's efforts to score, but he missed the target with only Oliver Baumann to beat.
He then tested the Freiburg goalkeeper before the break with a powerful shot from the edge of the penalty area.
Baumann was at full-stretch to push Rafael van der Vaart's direct free-kick away early in the second half before Son wasted another good chance, his third of the game.
Freiburg finally found a way through to take the lead in the 69th minute on the counter attack.
Mensur Mujdza set up Schmid, who beat Adler for his seventh goal of the season.
It was enough to earn Freiburg all three points, despite late chances from Son and Van der Vaart which again failed to hit the target.