Triple negative breast cancer (TNBC) is one of the most aggressive subtypes of breast cancer with the worst prognosis after chemo- or radiation therapy. This is mainly due to the development of cancer chemoresistance accompanied by tumor recurrence. In this work, we investigated a new mechanism of acquired chemoresistance of TNBC cells. We showed that extracellular vehicles (EVs) of chemoresistant TNBC cells can transfer mitochondria to sensitive cancer cells, thus increasing their chemoresistance. Such transfer, but with less efficiency, can be carried out over short distances using tunneling nanotubes. In addition, we showed that exosome fractions carrying mitochondria from resistant TNBC cells contribute to acquired chemoresistance by increasing mtDNA levels with mutations in the mtND4 gene responsible for tumorigenesis. Blocking mitochondrial transport by exosome inhibitors, including GW4869, reduced acquired TNBC chemoresistance. These results could lead to the identification of new molecular targets necessary for more effective treatment of this type of cancer.