Hamburg took their time to get going but second-half strikes from Vincent Kompany, Rafael van der Vaart, Collin Benjamin and David Jarolim secured the win.
FC Utrecht from Holland were upset by Swedish side Hammarby though, as a 1-1 home draw saw them lose out on the away goals rule after a goalless first leg.
Robin Nelisse had given the Dutch side the lead but David Johansson quickly equalised and Sander Keller was then sent-off as Utrecht couldn't get the crucial winner despite dominating.
Partizan UEFA Cup ban confirmed
A late goal from former Wigan man Andreas Johnansson sent Danish side AaB through to the UEFA Cup with a 2-1 (3-2 agg) victory over Belgian side AA Gent.
European football stalwarts Rapid Vienna will again return to the UEFA cup as a 0-0 draw at Russian side Rubin Kazan saw them go through 3-1 on aggregate.
Tobol Kostanay of Kazakhstan won 1-0 in Greece against OFI Crete to complete a 2-0 aggregate success, while Uniao Leiria came back from a 1-0 deficit to Hajduk Kula in the first leg to thrash the Serbian side 4-1 in Portugal.
Partizan allowed to play
Blackburn cruise to UEFA spot