The visitors took the lead just before the half-hour with a fine counter-attacking move which was finished off by Elias Kachunga for his second goal of the season. The former Hertha Berlin striker thought he had doubled the Bundesliga newcomers' lead just five minutes later, but his header was ruled out for offside by the assistant referee.
Hamburg should have levelled the score on 62 minutes when Marcell Jansen's cross from the left-hand side was met inside the six-yard box by Pierre-Michel Lasogga, but the striker failed to hit the target with the goal at his mercy. Lasogga's miss proved crucial, too, when Mario Vrancic intercepted Artjoms Rudnevs' wayward pass in midfield before rounding Rene Adler and firing into an empty net to double Paderborn's lead.
Rudnevs almost atoned for his earlier error late on when he set up Ivo Ilicevic, but Lukas Kruse did well to keep out the Croatian's effort. The visitors put the seal on their first ever Bundesliga with three minutes remaining, Moritz Stoppelkamp firing past Rene Adler to complete a memorable win.
Line-ups and statistics