Caiuby gave the visitors an early lead before Christian Clemens and Pablo de Blasis put Mainz 2-1 up.
Ja-Cheol Koo restored parity but de Blasis and Clemens secured their braces in the second half to seal a 4-2 win.
Level-pegging at the break
After Yunus Malli missed the chance to chip Marwin Hitz, Augsburg managed to storm up the other end and open the scoring.
Markus Weinzierl gave his side the hurry up by encouraging a quick throw-in. The ball eventually found Alfred Finnbogason bursting through the middle, though he was hacked down on the edge of the area. Patrick Ittrich played advantage, the ball carried on moving and Caiuby made it count, slotting the ball home coolly with a fine finish.
Mainz weren't behind for long, and four minutes later parity was restored. Clemens came in from the right and exchanged passes with Malli, before bringing the ball inside and firing past Hitz. The hosts took full advantage of some sluggish Augsburg defending, which came about from their snappy passing.
Their first goal was class, but Mainz's second full a comedy of defensive errors from their opponents. After Dominik Kohr lost the ball, Jeong-Ho Hong only succeeded in missing his clearance that Danny Latza managed to slide through to de Blasis. The Argentine rounded Hitz and slid the ball into an open net.
There was a turning point late on in the half, as some more stylish play from Mainz saw Jhon Cordoba go through on goal. Hitz, however, produced a fantastic stop. From there, Markus Feulner was given space to pick out Koo. The former Mainz man touched the ball past his defender and rifle the ball under the bar to level before the break.
De Blasis and Clemens secure a vital three points
Mainz didn't have to wait long until they got back in front for a second time. De Blasis was on hand to head home his second goal of the game, after waiting five months since his last strike, after some excellent play by Daniel Brosinski. He hustled his way down the wing before standing up a cross to the back post, which was duly dispatched.
Caiuby offered up hope of an equaliser for Augsburg, but his crosses couldn't quite find their target. The second of which did drop kindly to Raul Bobadilla, though Loris Karius was able to produce a vital save.
With the visitors coming forward in waves, Mainz were able to bide their time and scramble on the counter. De Blasis and Cordoba played the final two key passes as they sped up the pitch, leaving Clemens to slot past the oncoming Hitz and seal the three points.
The Karneval club's unlikely Champions League hopes are slowly becoming a real possibility, though Augsburg are dropping dangerously close to the bottom.