(1) Background: Triple negative breast cancer (TNBC) is a highly aggressive tumor, associated with high rates of early distant recurrence and short survival times, and treatment may require surgery, and thus anesthesia. The effects of anesthetic drugs on cancer progression are under scrutiny, but published data are controversial, and the involved mechanisms unclear. Anesthetic agents have been shown to modulate several molecular cascades, including PI3K/AKT/mTOR. AKT isoforms are frequently amplified in various malignant tumors and associated with malignant cell survival, proliferation and invasion. Their activation is often observed in human cancers and is associated with decreased survival rate. Certain anesthetics are known to affect hypoxia cell signaling mechanisms by upregulating hypoxia-inducible factors (HIFs). (2) Methods: MCF-10A and MDA-MB 231 cells were cultivated and CellTiter-Blue® Cell Viability assay, 2D and 3D matrigel assay, immunofluorescence assays and gene expressions assay were performed after exposure to different sevoflurane concentrations. (3) Results: Sevoflurane exposure of TNBC cells results in morphological and behavioral changes. Sevoflurane differently influences the AKT isoforms expression in a time-dependent manner, with an important early AKT3 upregulation. The most significant effects occur at 72 h after 2 mM sevoflurane treatment and consist in increased viability, proliferation and aggressiveness and increased vimentin and HIF expression. (4) Conclusions: Sevoflurane exposure during surgery may contribute to cancer recurrence via AKT3 induced epithelial–mesenchymal transition (EMT) and by all three AKT isoforms enhanced cancer cell survival and proliferation.