The adaptive treatment tolerance (ATT) of cancer cells is the main encumbrance to cancer chemotherapy. A potential solution to this problem is to treat cancer cells with multiple drugs using nanoparticles (NPs). In this study, we tested the co-administration of curcumin (Cur) and doxorubicin (Dox) to MCF-7 resistant breast cancer cells to block the ATT and elicit efficient cell killing. Drugs were co-administered to cells both sequentially and simultaneously. Sequential drug co-administration was carried out by pre-treating the cells with albumin nanoparticles (ANPs) loaded with Cur (Cur@ANPs) followed by treatment with Dox-loaded ANPs (Dox@ANPs). Simultaneous drug co-administration was carried out by treating the cells with ANPs loaded with both the drugs (Cur/Dox@ANPs). We found that the simultaneous drug co-administration led to a greater intra-cellular accumulation of Dox and cell killing with respect to the sequential drug co-administration. However, the simultaneous drug co-administration led to a lower intra-cellular accumulation of Cur with respect to the sequential drug co-administration. We showed that this result was due to the aggregation and entrapment of Cur in the lysosomes as soon as it was released from Cur@ANPs, a phenomenon called lysosomotropism. In contrast, the simultaneous release of Dox and Cur from Cur/Dox@ANPs into the lysosomes led to lysosomal pH elevation, which, in turn, avoided Cur aggregation, led to lysosome swelling and drug release in the cytosol, and finally provoked efficient cell killing. Our study shed the light on the molecular processes driving the therapeutic effects of anti-cancer drugs co-administered to cancer cells in different manners.