Ingolstadt have been relegated from the Bundesliga as a result of their 1-1 draw with Freiburg on Saturday.
The stalemate at Schwarzwald Stadion had looked set to be good enough to keep them alive heading into the final week of matches, with Hamburg losing 1-0 to Schalke at Veltins Arena.
However, an injury-time equaliser from Pierre-Michel Lasogga snatched a draw for HSV that ensures they stay four points above Ingolstadt in the table and confirms the latter's relegation.
Ingolstadt fans thought they had been granted a reprieve when news filtered through of a stoppage-time Schalke goal from Sead Kolasinac, but it was ruled out after Lewis Holtby's corner was adjudged to have gone out of play before being turned in by the defender.
Maik Walpurgis' side, who won the 2.Bundesliga title in May 2015 to secure promotion to the top flight, will join Darmstadt in dropping down to the second tier for next season.
Hamburg can still climb out of the relegation play-off spot if they beat Wolfsburg on the final day of the season, with Andries Jonker's side having drawn 1-1 at Borussia Monchengladbach after a lengthy stoppage in play due to a hail storm.
