Reducing carbon emissions from power batteries is essential for the low-carbon development of electric vehicles (EVs). In response to the carbon labeling requirements of the EU battery regulation, this study developed a three-tiered supply chain model incorporating the battery material supplier, the power battery manufacturer, and the EV company. Using Stackelberg game theory, the research evaluated four carbon emission reduction strategies and analyzed the impact of consumer environmental awareness on carbon emissions. The results reveal that for batteries with lower initial carbon footprints, increased consumer environmental awareness is associated with a reduction in carbon emissions. For batteries with higher initial carbon footprints, the relationship between consumer environmental awareness and carbon emissions is more complex. Below a certain threshold, higher environmental awareness leads to carbon emission reduction; however, beyond this threshold, increased environmental awareness can elevate carbon emissions. Moreover, under low consumer environmental awareness, a strategy of comprehensive collaboration among all supply chain tiers yields the highest economic benefits, albeit with higher emissions. As environmental awareness rises, the strategy where the material supplier independently reduces emissions and the battery manufacturer and EV company collaborate on emission reductions emerges as the most effective, striking an optimal balance between economic and environmental interests.