The Bavarians, backed by car maker Audi and officially the youngest club in the professional leagues after being formed in 2004, are now seven points clear at the top with a game to spare.
Ingolstadt came from a goal down to level with Australian Mathew Leckie. Stefan Lex snatched the winner in the 76th when Leipzig keeper Benjamin Bellot let the ball slip through his hands.
Ingolstadt, with Audi owning a stake in the club and the stadium they play in, shot up the lower leagues since 2004, winning their first promotion to the second tier in 2009.
They were relegated the season after but went straight back up before completing their rise to fame with their most memorable win to date on Sunday.
Second-placed Darmstadt, on 56, and Kaiserslautern and Karlsruhe, both on 55, will battle it out for the other automatic spot and the third place that leads to a promotion playoff.
(Reporting by Karolos Grohmann, editing by Ed Osmond)
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