  We propose a generic scenario for realizing gapful topological
superconductors (TSCs) from gapless spin-singlet superconductors (SCs).
Noncentrosymmetric nodal SCs in two dimension are shown to be gapful under a
Zeeman field, as a result of the cooperation of inversion-symmetry breaking and
time-reversal-symmetry breaking. In particular, non-s-wave SCs acquire a large
excitation gap. Such paramagnetically-induced gapful SCs may be classified into
TSCs in the symmetry class D specified by the Chern number. We show nontrivial
Chern numbers over a wide parameter range for spin-singlet SCs. A variety of
the paramagnetically-induced gapful TSCs are demonstrated, including D+p-wave
TSC, extended S+p-wave TSC, p+D+f-wave TSC, and s+P-wave TSC. Natural extension
toward three-dimensional Weyl SCs is also discussed.
