Hamburg pushed Hoffenheim closer to the 2. Bundesliga with a convincing win which keeps their own hopes of European football next season alive going into the final round of matches next weekend.
Son Heung-min, Dennis Aogo, Petr Jiracek and Arjoms Rudnevs were all on target for Thorsten Fink's men with Kevin Volland's goal worthless for a Hoffenheim side who remain two points adrift of safety and now needing something special to avoid relegation.
They travel to Champions League finalists Borussia Dortmund next weekend needing to win and hope either Fortuna Dusseldorf or Augsburg are unsuccessful in their matches.
Hamburg, meanwhile, host Leverkusen knowing a win could take them past Eintracht Frankfurt into sixth place.
Son nearly put Hamburg in front in the third minute of an open game which both sides clearly wanted to win.
Sejad Salihovic went close for Hoffenheim with a long-range effort which only just went wide.
Son's second chance of the game landed in the back of the net in the 18th minute as he headed Hamburg in front from Dennis Diekmeier's cross.
Jiracek should have doubled Hamburg's lead in the 28th minute, but he shot wide with only Koen Casteels to beat.
The second Hamburg goal was not far away, though, and in the 35th minute, Aogo got it.
Son dribbled round Casteels and unselfishly played the ball square to the Germany international, who tapped the ball into an unguarded goal.
Hoffenheim's hopes of a recovery were effectively ended on the hour mark when the ball somehow found its way through to Jiracek, who scored from close range.
Just a minute later, Volland reduced the arrears from eight yards.
The hosts threw caution to the wind, knowing they needed to find two goals inside the last 10 minutes.
That left them open at the back, though, and Hamburg finished them off on the counter-attack in the 88th minute.
Milan Badelj sent Rudnevs through, and he got the better of Casteels in a one-on-one situation to complete the scoring.