Armin Veh's charges had gone 10 Bundesliga matches without a win before the shock 1-0 triumph against Leverkusen on Sunday.
On this occasion, Frankfurt needed to come from behind simply to secure a share of the spoils, having fallen behind at the Commerzbank-Arena in the 32nd minute.
Raul Bobadilla pounced on a loose ball in the box to side-foot a volley beyond Kevin Trapp from six yards and give Augsburg the lead.
Yet Frankfurt were soon level as Jan Rosenthal fired home an equaliser three minutes before the break.
There were few clear-cut opportunities in the second half and both sides had to settle for a point apiece, leaving Frankfurt in 15th while Augsburg remain eighth.
‘The pure simplicity of the way Slot has managed the squad is probably the biggest thing I could say about him. It’s not broken, so let’s get on with it’: Liverpool legend full of admiration for Jurgen Klopp's successor at Anfield
‘I trained at Spurs and thought they’d give me a chance. But I received a letter thanking me but saying they didn’t think I was good enough – I was gutted’: How Tottenham missed out on signing Wales legend John Toshack
