كتب : Hatem Maher
Croatian striker Ivica Olic put the visitors in front in the 17th minute and skipper Rafael van der Vaart doubled the lead in the 26th minute.
Olic struck home again six minutes after restart to put the result beyond doubt. An own goal by Joris Mathijsen in the 75th minute gave Rostock a consolation.
Egyptian forward Zidan did not take part in the game due to illness, Hamburg said on their website.
The victory put Hamburg in fourth place of the league table with 51 points, four adrift of third-placed Schalke, who were held to a 1-1 draw with Hanover 96.
With three matches to go, Hamburg have a chance to leapfrog Schalke and claim the final Champions League qualifying spot.
Elsewhere, Werder Bremen cemented their second-place position after a 2-0 victory over Energie Cottbus.
Two second-half goals from Rosenberg and Hugo Almeida were enough for Bremen to win.
Bremen are nine points behind leaders Bayern Munich, who need just a draw against Wolfsburg on Sunday to wrap up their 21st Bundesliga title.