While the stalemate looked like it would be enough to keep Maik Walpurgis' side alive heading into the final round of matches, an injury time equaliser scored by Pierre-Michel Lasogga snatched a late draw for Hamburg while ensuring they stay four points above Leckie's side - enough to confirm the latter's relegation.
Ingolstadt, who won the 2.Bundesliga title in 2015 to secure promotion to the top flight, will join Darmstadt in dropping down to the second tier for next season.
Despite performing well in their initial campaign back in the top flight, finishing 11th, the side have struggled since former coach Ralph Hasenhuttl left for RB Leipzig last May, winning only eight of their 33 league games to date this term.
Ingolstadt thanked fans for supporting the team during their two year Bundesliga run in a post on Twitter.
Hamburg meanwhile are still able to climb out of the relegation play-off spot should 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.