  We calculate the time-like pion-photon transition form factor and the pion
electromagnetic form factor up to next-to-leading order (NLO) of the strong
coupling constant in the leading-twist $k_T$ factorization formalism. It is
found that the NLO corrections to the magnitude (phase) are lower than 30%
($30^\circ$) for the former, and lower than 25% ($10^\circ$) for the latter at
large invariant mass squared $Q^2>30$ GeV$^2$ of the virtual photons. The
increase of the strong phases with $Q^2$ is obtained, consistent with the
tendency indicated by experimental data. This behavior is attributed to the
inclusion of parton transverse momenta $k_T$, implying that the $k_T$
factorization is an appropriate framework for analyzing complex time-like form
factors. Potential extensions of our formalism to two-body and three-body
hadronic $B$ meson decays are pointed out.
