Unsymmetrical squaraine dyes (CTSQ-1 and CTSQ-2) with carbazole thiophene donor units were synthesized, characterized and used as sensitizers in dye-sensitized solar cells (DSSCs). These squaraines exhibited intense absorption in the near IR-visible region of the solar spectrum both in solution and on TiO2 surface. The LUMO level of the parent sensitizer (CTSQ-2) was positioned at a potential much close to the conduction band of TiO2 resulting in lack of enough driving force for electron injection which was modulated by structurally changing the donor carbazole moiety (CTSQ-1), pushing the LUMO more positive thereby enhancing the driving force. Theoretical calculations were carried out in order to have a better understanding of the electron density distribution in CTSQ-1 and CTSQ-2. Electron injection dynamics in CTSQ-1 was studied in detail by changing the Li(+) concentration and its effects on photovoltaic parameters were discussed with the help of JV, IPCE, lifetime and EIS measurements.