Mainz, who are fifth on 31 points, struggled to settle into the game with Augsburg who were out to extend their four-game unbeaten run that has helped them off the bottom spot and close in on the relegation play-off berth.
The visitors broke the deadlock just before the break, taking advantage of a lapse of concentration in the Augsburg defence after right back Ronny Philip was stretchered off and American Michael Parkhurst replaced him.
Adam Szalai was left unmarked, lurking at the far post when two defenders failed to clear a seemingly harmless cross and the Hungarian drilled in for the lead with his 12th league goal of the campaign.
Mainz, however, were left with 10 men minutes later when Shawn Parker was sent off for a rough challenge on Parkhurst and the hosts quickly made the extra man count when Sascha Moelders headed in from 10 metres to level in the 57th.
Augsburg are still 17th in the league but have now moved to within a point of Hoffenheim, in 16th.
Bayern Munich are cruising towards their first Bundesliga title since 2010 after crushing Schalke 4-0 on Saturday to open up a 15-point lead over champions Borussia Dortmund, who suffered a 4-1 home loss to Hamburg and have 39 points.
Bayer Leverkusen stayed in third place on 38 after conceding a late equaliser in their 3-3 draw at Borussia Moenchengladbach.