Andrea Hahn scored both goals for the home team, who moved level on point with their opponents in mid-table.
Eric Maxim Choupo-Moting replied from the penalty spot while Mainz lost goalkeeper Christian Wetklo to a red card late on, compounding their misery in Bavaria.
Augsburg started the game brightly, but Mainz hit back well to force the first chances of the game.
Shinji Okazaki, whose two goals got the better of Braunschweig a week ago, got two bites of the cherry with the first big chance, falling to the floor to start with, but getting back on his feet to skip past Jan-Ingwer Callsen-Bracker only to shoot straight at Marwin Hitz.
Soon after, Sebastian Polter's shot on the volley was saved well by Hitz.
As Mainz were just beginning to get on top of the game, Hahn put Augsburg in front, beating the offside trap to touch Daniel Baier's long ball down with his chest and sweep it under Christian Wetklo in the Mainz goal.
Hahn again broke the offside trap in the 49th minute before attempting to take the ball round Wetklo, who managed to get a hand to the ball to push it wide.
Hahn did not give up, though, and he picked up the loose ball and curled it into the unguarded goal from a tight angle.
Halil Altintop almost made it three when he lobbed Wetklo from 10 yards, but the ball bounced back off the bar.
Moments after, Polter had his shirt tugged in the area by Callsen-Bracker and Choupo-Moting, who had only just entered the fray from the substitutes' bench, swept the resulting penalty in.
The game was wide open, but Arkadiusz Milik could have finished Mainz off had Wetklo not made a save.
The Mainz goalkeeper then got a rush of blood to the head as he came out of his area, misjudging the bounce of the ball and sending Milik tumbling to earn a red card.
With all the substitutions having been made, Polter went in goal and he made a fine save from the resulting free-kick to keep Mainz's hopes alive, although their late surge failed to yield an equaliser as Augsburg held on.