"We want to show against Wolfsburg this Sunday that we are going to exhaust all of our opportunities (to qualify for Europe)," said Hamburg's coach Thorsten Fink.
"And then if the other teams around us do the same, and are better in the end, then we can also lose, but at least we can say we gave it a go."
On Friday, Schalke consolidated fourth place in the Bundesliga thanks to a 1-0 win at Borussia Monchengladbach which dented the Foals' hopes of playing in Europe next season.
The Champions League final dress rehearsal between Borussia Dortmund and Bayern Munich ended all square on Saturday while Bayer Leverkusen sealed their top four spot.
Dortmund went ahead through Kevin Grosskreutz after 11 minutes, only for Mario Gomez to level after 23 minutes.
Rafinha was dismissed four minutes later after picking up two yellow cards in the space of three minutes.
Elsewhere, Stefan Kiessling scored against his former employers to break a new club goalscoring record and take Bayer Leverkusen into the Champions League next season with a 2-0 win at Nuremberg.
Two goals from Alexander Meier and a Srdjan Lakic strike helped Eintracht Frankfurt beat Fortuna Dusseldorf 3-1 and remain on course for a a place in the Europa League next season.
Hoffenheim fought back from two goals down to keep their survival hopes alive in dramatic fashion with a 2-2 draw at fellow strugglers Werder Bremen.
Hannover and Mainz drew 2-2 at the AWD-Arena as both sides' slim hopes of European football next season all but disappeared.
Relegated Greuther Furth stunned Stuttgart 2-0 to clinch only their fourth league win of the season.
Sunday's Bundesliga Fixtures
Hamburg vs Wolfsburg
Saturday's Bundesliga Results
Friday's Bundesliga Result