With their only goal in this season’s competition coming via an own goal against Stade Brestois on the opening matchday, the hosts came close to finally scoring for themselves shortly before the 15th minute.
In sensational form this season, Biereth - who currently tops the Austrian Bundesliga scoring charts with 10 goals - nearly opened his maiden account in the UCL. However, Paulo Gazzaniga was ready for the former Arsenal striker as he expertly kept out a sweetly-struck effort.
Girona’s response was almost immediate, but Bojan Miovski could only send his header high into the stands despite being unmarked in the area.
Back at the opposite end, Sturm saw another chance wasted as William Boving fired a solo effort millimetres wide of the post. That trend continued, with Gazzaniga preventing Dimitri Lavalee’s thunderbolt on the brink of half-time.
Looking to register a fifth victory in six matches across all competitions, Girona were left bemoaning their luck seven minutes into the second half as stand-in skipper Juanpe saw his effort chalked off for offside in the build-up.
The Blanquivermells were then left cursing their misfortune shortly before the hour mark, with Biereth positioning himself well to fire Sturm ahead after Gazzaniga failed to keep hold of the initial effort from Seedy Jatta.
Remarkably, Girona hit back almost immediately from the restart when Alejandro Frances produced some silky skills, marauding forward from full-back before firing wide of the mark.
A late header from substitute Cristhian Stuani that was easily held by Daniil Khudyakov turned out to be Girona’s final chance of salvaging a point.
The landmark victory sees Sturm record their first-ever success over Spanish opposition and in the process, move Jurgen Saumel's side to within two points of the play-off positions.
Conversely, the defeat sees Girona write an unwanted narrative for Spanish football in the UCL, as the Blanquivermells become the first-ever side to lose all three of their opening away games.