Raul Bobadilla gave the Bavarians the lead at the Waldstadion, but Jan Rosenthal levelled for the hosts.
Augsburg substitute Arkadiusz Milik then wasted a gilt-edged chance late on to earn his side all three points, although a late penalty appeal left Frankfurt fuming and nobody happy with just a point.
Former Frankfurt goalkeeper Oka Nikolov was given an emotional send off before the game as he returned to the one and only club he represented in his playing career in Germany after a six- month career-ending spell in the USA.
He took his place in the stands to see some rather sub-standard football too early on with neither side able to create any chances.
That persisted until a mistake by Pirmin Schwegler teed up Bobadilla for an easy finish past Kevin Trapp to give Augsburg the lead in the 33rd minute.
Frankfurt responded well and it took a fine save from Marwin Hitz to prevent Joselu from levelling shortly after, the ball also grazing the post on its way wide.
Hitz then denied Stephan Schrock's header as the hosts increased the pressure, reaping their reward just before half-time when Schwegler's cross was deflected by Joselu and landed in front of Rosenthal, who volleyed it in without hesitation.
The second half saw Alexander Meier return to the Frankfurt team after a four-week lay-off, but he was unable to inspire a win.
Instead, Frankfurt were lucky not to be beaten when Milik was allowed acres of space to bear down on Trapp, only to be denied with a tame effort.
Trapp also saved his follow-up with Carlos Zambrano covering to clear the ball as it looped towards the open goal.
In the dying seconds, Frankfurt then demanded a penalty when a Constant Djakpa cross struck the arm of Jan-Ingwer Callsen-Bracker, but the referee adjudged the touch involuntary and, moments later, brought the game to an end.