Defenceman Kevin Klein, right-winger Rich Peverley and centre Jason Guerriero scored in regulation for Milwaukee. Peverley and Guerriero, who also scored in the shootout, each added a helper for two-point games, while Koistinen had two assists.
Right-wingers Martin Sagat, with his first goal of the season, and Jeff Corey and "left-winger Colin Murphy scored for the Marlies in front of 3,861 fans at Ricoh Coliseum.
Centre Kris Newbury collected two assists. Murphy also scored in the shootout, but was the only Marlie to beat Goehring in the 1-on-1 format.
The Admirals improved to 9-11-2 on the season, while the Marlies fell to 9-11-4.
Toronto netminder Jean-Francois Racine stopped 21 of 24 shots, but it was Goehring who kept his team in the game in the first period when Toronto threatened to rout the Admirals.
The Marlies led 2-0 after the first - and dominated the frame, outshooting Milwaukee 19-2 - before the Admirals rallied to tie the game 2-2 after 40 minutes.
The Marlies went 1-for-7 on the power play, while the Admirals went 2-for-8 with the man advantage.
The Marlies are off until Wednesday, when they host their provincial and North Division rival, the Hamilton Bulldogs.