The Berlin club won 0-2, perfectly launched by Belgian captain Dedryck Boyata, who scored in the 4th minute with a crossed header from a corner.
The 31-year-old Belgian defender chose his moment well to plant his first goal of the season. Marvin Plattenhardt sealed the match by doubling his lead shortly after the hour mark. The German defender, already a decisive passer for the Red Devil at the start of the game, sent a direct free kick into the top corner opposite, coming to air-condition a Volksparkstadion yet white-hot (63rd).
Hamburg SV, which left the top flight four seasons ago and finished 3rd in D2 this season, will still have to wait before returning to the top flight.
The two directly promoted to the Bundesliga are Schalke and Werder Bremen, and the two relegated to the 2nd division, Bielefeld and Fürth.