The South Korean, who joined Augsburg on loan from Wolfsburg during the January transfer window, has been a big hit for the battling club who have revived their hopes of survival in recent weeks.
Mainz had gone ahead through Sami Allagui on 36 minutes, before Koo responded with a sensational strike two minutes prior to the interval.
Torsten Oehrl's flick found Koo just outside the box and he teed himself up to strike a fine volleyed effort from distance which nestled into the top corner.
Sebastian Langkamp got what proved to be the winner on 51 minutes, while Koo was replaced with eight minutes to go.
Elsewhere in the Bundesliga, Son Heung-Min made an impressive impact off the bench after coming on as a half-time substitute with Hamburg trailing Freiburg 2-0.
Son, who replaced Robert Tesche at the break, firstly sent an 18-yard shot wide on 55 minutes.
Moments later his left-wing cross picked out Mladen Petric with an open goal but the Croatian somehow pushed it wide. Freiburg would go on to win the game 3-1.
|STAR OF THE WEEKEND
Continues to win over the Augsburg faithful with another important strike in their bid to avoid the drop
Lee Chung-Yong (Bolton): Out injured (leg) for the FA Cup clash with Tottenham which was abandoned after Fabrice Muamba collapsed late in the first half.
Park Chu-Young (Arsenal): The Gunners were not in action this weekend.
Park Ji-Sung (Manchester United): Was an unused substitute in the 5-0 win away to Wolverhampton in the Premier League.
Yu Tae-Sun (FSV Frankfurt): Was an 84th-minute substitute in the 0-0 draw at Eintracht Braunschweig.
Jung Jo-Gook (Nancy): Was left on the bench as his side pulled off a shock 1-0 victory over title hopefuls Montpellier.
Suk Hyun-Jun (FC Groningen): Was a 57th-minute substitute in the 3-1 loss away to FC Utrecht.
Kim In-Sung (CSKA Moscow): Scheduled to play Spartak Moscow on Monday.
Cha Du-Ri (Celtic): Was an unused substitute in their shock 1-0 League Cup final defeat to Kilmarnock.
Ki Sung-Yueng (Celtic): Came on as a 53rd-minute substitute and from his corner Victor Wanyama forced a fine save out of Kilmarnock keeper Cameron Bell. But ultimately it was disappointment after conceding late to lose to Kilmarnock and end their hopes of a treble.
Cho Yong-Hyung (Al Rayyan): Played a full game, picking up a 52nd-minute booking, in his side's 3-2 loss at El Jaish.
Lee Jung-Soo (Al Sadd): Put in a full shift as his side came from three goals down to draw 3-3 with Qatar SC.
Nam Tae-Hee (Lekhwiya): Played a full game in the 3-1 win at Umm Salal, which all but seals the title, with Lekhwiya nine points clear with three games to play.
Yoo Byung-Soo (Al Hilal): Played a full game and netted a double in his side's 6-1 win over Al Ansar. Yoo scored the opener on 37 minutes, and added their fourth on 66 minutes.
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