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.
Ingolstadt performed impressively in their first campaign back in the top flight, finishing 11th in the table and only 10 points shy of the European places.
They have struggled since head coach Ralph Hasenhuttl, who left for RB Leipzig last May, however, winning only eight of their 33 league games to date this term.