The two sides headed into the game with identical records, having taken three wins from their first six games, and there was nothing to separate them in Friday's meeting at the SGL Arena.
Augsburg had taken the lead through winger Andre Hahn, but Gladbach looked to be on their way to victory after Max Kruse and Branimir Hrgota had turned things around, only for Polish striker Milik to deny them the points with a close-range strike.
The hosts started the game the better of the two sides, and they went close early on as Halil Altintop fired wide with a low volley.
Winger Juan Arango crashed a shot against the crossbar as Gladbach grew into the game, but it was Augsburg who seized the initiative after 27 minutes, Hahn firing past Marc-Andre ter Stegen at the near post after being played through by Tobias Werner.
It took the visitors just six minutes to level, though, attacking midfielder Kruse converting from Christoph Kramer's pull back after good work from Raffael.
The scores remained level until the break, but midway through the second half, Swedish attacker Hrgota met Kruse's left-wing cross with a wonderful driven effort that flew past Alex Manninger and into the bottom corner.
Augsburg began to dictate the game as they pushed for the equaliser and two minutes from time they get their reward, Milik collecting Hahn's far-post delivery to tap in and ensure a share of the spoils.
