Marko Marin, Tom Trybull and Marko Arnautovic scored the goals as Thomas Schaaf's side posted victory at the HSV-Arena.
Mladen Petric's goal, which made it 2-1 in the 76th minute, was mere consolation for the home side, who remain in the bottom half of the table while Werder cement their hold on fifth place.
Werder took the lead in the ninth minute through Marin, who picked his spot inside Jaroslav Drobny's near post after a good run and pass from Markus Rosenberg.
Hamburg reacted well and almost levelled when Jose Guerrero's volley was saved well by Tim Wiese before Drobny made a good save at the other end to deny Rosenberg in an open start to the game.
Arnautovic adds a third
Guerrero and Petric both missed the target before Werder doubled their lead on the stroke of half-time, Zlatko Junuzovic's corner headed in by Trybull with his first goal for the club.
Hamburg were not going to lie down, though, and Dennis Aogo's free-kick in the 50th minute almost brought them back into the game. Ivo Ilicevic came even closer to scoring when his shot hit the woodwork before Petric gave the home fans hope in the 76th minute.
His direct free-kick found its way through the Werder wall, taking a deflection on its way with Wiese beaten. Hamburg's hopes were dashed in the 86th minute when Arnautovic made it three and sealed Werder's victory.
It was route-one stuff, with Wiese's long punt forwards finding its way through to Arnautovic, who took advantage of a defensive misunderstanding to bear down on Drobny and coolly slot the ball in.