The winger's goal 12 minutes after Hildur Antonsdottir's second-half dismissal was enough to earn the Fins a narrow win in a tense tournament opener in Thun.
Kosola had already gone close in the opening period, forcing Iceland goalkeeper Cecilia Ran Runarsdottir into a good save, before firing a presentable chance over the top.
Iceland threatened themselves with a couple of goalmouth scrambles, but the game changed in the 58th minute when Antonsdottir was sent off for a second bookable offence, catching her opponent on the top of the foot having already seen yellow for taking Kosola out just six minutes earlier.
Finland took charge from there and Kosola made the player advantage count, driving a rasping effort into the top corner on 70 minutes to give her side a priceless lead.
The Fins avoided any late drama to seal the victory and put themselves in a fine position in Group A. This was Finland's first win at a European Championship since 2009.