Dortmund twice went ahead on goals by Sven Bender in the sixth minute and Nuri Sahin after 66 minute, but Bender scored an own goal in the 56th minute and Ji Dong Won equalised at 2-2 in the 72nd minute for the visitors.
Dortmund moved to 33 points - four points behind Leverkusen - in third place, while Augsburg picked up a point to improve to 25.
The draw also saw Dortmund midfielder Jakub Blaszczykowski get subbed off after just six minutes with the initial diagnosis of a torn knee ligament.
The home side took the lead after six minutes from a set piece with Marco Reus sending his free-kick from the left to the far right side to a charging Bender, who headed past Augsburg goalkeeper Marwin Hitz.
Dortmund had to sub off Blaszczykowski directly after the goal with what the team fears is a torn knee ligament.
The hosts were close to doubling the lead in the 23rd minute as Reus' free-kick went to the far left post where Sokratis headed wide.
Dortmund nearly struck again six minutes later but Henrikh Mkhitaryan's shot went wide right.
Augsburg made Dortmund pay for not using their chances and equalised in the 56th minute - albeit on an own goal as Bender tried to clear Andre Hahn's cross from the right but it went into his own goal.
Dortmund went back ahead in the 66th minute as Sahin circled his free-kick over the wall and into the upper right corner to make it 2-1.
But Augsburg equalised again in the 72nd minute with Ji heading in Hahn's cross.
The South Korean, who will play for Dortmund next season, was came on a s a substitute just two minutes earlier.
Dortmund's final chance came with 15 minutes left but Robert Lewandowski's header sailed over the bar.