One concept of improving anticancer effects of conventional platinum-based antitumor drugs consists of conjugating these compounds with other biologically (antitumor) active agents, acting by a different mechanism. Here, we present synthesis, physicochemical characterization, biological effects, and mechanisms of action of four new analogs of conventional cisplatin, namely, cis-Pt(II) complexes containing either methyl or ethyl pyrazole N-donor ligands and chlorido or iodido ligands. It is noteworthy that while chlorido complexes display activity in a variety of cancer cell lines comparable to cisplatin, iodido complexes are considerably more potent due to their enhanced hydrophobicity and consequently enhanced cellular accumulation. Moreover, all of the studied Pt(II) alkylpyrazole complexes display a higher selectivity for tumor cells and effectively overcome the acquired resistance to cisplatin. Further results focused on the mechanism of action of the studied complexes and showed that in contrast to cisplatin and several platinum-based antitumor drugs, DNA damage by the investigated Pt(II)-alkylpyrazole complexes does not play a major role in their mechanism of action. Our findings demonstrate that inhibition of the tubulin kinesin Eg5, which is essential for forming a functional mitotic spindle, plays an important role in their mechanism of antiproliferative action.