  We discover superconductivity (SC) in LaAgSb$_2$ at ambient pressure and its
close correlation with a charge density wave (CDW) under pressure. The
superconducting transition temperature ($T_c$) exhibits a sharp peak at the CDW
critical pressure of 3.2 GPa. We demonstrate that the carriers inhabiting the
Sb-square net is crucial not only in the formation of CDW but also in SC for
their relatively strong electron-phonon coupling (EPC). Furthermore,
theoretical EPC strength in pristine LaAgSb$_2$ cannot explain the observed
peak with $T_c\sim 1$ K, which indicates that an additional mechanism
reinforces SC only around the CDW critical pressure.
