Swiss winger Ruben Vargas gave Augsburg the lead with an outstanding bicycle kick simply earlier than half-time.
Mainz sub Karim Onisiwo equalised on the hour mark, however Augsburg took benefit of drained legs as Germany winger Hahn netted twice within the closing 10 minutes.
Werder Bremen coach Florian Kohfeldt picked up some extent on his third anniversary within the job with a 1-1 draw at Eintracht Frankfurt.
US striker Josh Sargent swept his shot dwelling early within the second half to present Bremen the lead.
Frankfurt’s Japan midfielder Daichi Kamada had a first-half purpose dominated out when VAR (video assistant referee) noticed Andre Silva was offside.
Nonetheless, the Portugal worldwide made amends when he buried Kamada’s cross into the Bremen web for the equaliser on 65 minutes.
Schalke, second from backside, has gone 22 league video games and not using a win after being held to a 1-1 draw at dwelling to Stuttgart on Saturday (AEDT).
A primary-half header by Schalke’s teenage defender Malick Thiaw was cancelled out by a leveller from Argentinian ahead Nicolas Gonzalez for the guests.
Schalke is edging in direction of the undesirable file of Tasmania Berlin, which now play in Germany’s fifth tier and went 31 Bundesliga matches with out victory within the 1965-1966 season.