It appeared that Augsburg were on course for just their second league win of the season as they bounced back from two goals behind to take the lead late on, but Muto stunned the home fans to snatch a point for Mainz.
The Japanese forward was a threat to the Augsburg defence from the first whistle, and he broke the deadlock 18 minutes into the game by slotting home after Pablo De Blasis had held off a challenge to deliver the cross from the byline.
It was a case of being in the right place at the right time on the half-hour mark when Jairo Samperio's miscued shot sent the ball into the path of Muto, who showed his composure to convert at the back post.
Despite looking vulnerable to every Mainz attack, Augsburg were gifted the chance to get back in the game before the break after De Blasis was adjudged to have handled the ball while charging down Daniel Baier's powerful strike.
Paul Verhaegh took on the responsibility from 12 yards and fired his effort into the bottom corner to reduce the deficit.
Ausgburg needed just five second-half minutes to get back on level terms as Francisco Caiuby delivered an inch-perfect cross to Koo Ja-Cheol, who capitalised on poor marking to volley home the equaliser against his former side.
There would be one final twist on an enthralling afternoon as a long ball was flicked to Muto, who cut past one challenge in the box to find the bottom corner and silence the home supporters.