  Gamma-ray burst (GRB) 120729A was detected by Swift/BAT and Fermi/GBM, and
then rapidly observed by Swift/XRT, Swift/UVOT, and ground-based telescopes. It
had a single long and smooth \gamma-ray emission pulse, which extends
continuously to the X-rays. We report Lick/KAIT observations of the source, and
make temporal and spectral joint fits of the multiwavelength light curves of
GRB 120729A. It exhibits achromatic light-curve behavior, consistent with the
predictions of the external shock model. The light curves are decomposed into
four typical phases: onset bump (Phase I), normal decay (Phase II), shallow
decay (Phase III), and post-jet break (Phase IV). The spectral energy
distribution (SED) evolves from prompt \gamma-ray emission to the afterglow
with photon index from $\Gamma_{\rm \gamma}=1.36$ to $\Gamma \approx 1.75$.
There is no obvious evolution of the SED during the afterglow. The
multiwavelength light curves from \gamma-ray to optical can be well modeled
with an external shock by considering energy injection, and a time-dependent
microphysics model with $\epsilon_B\propto t^{\alpha_B}$ for the emission at
early times, $T < T_{\rm 0} + 157$~s. Therefore, we conclude that both the
prompt \gamma-ray emission and afterglow of GRB 120729A have the same external
shock physical origin. Our model indicates that the $\epsilon_B$ evolution can
be described as a broken power-law function with $\alpha_{\rm B,1} = 0.18 \pm
0.04$ and $\alpha_{\rm B,2} = 0.84 \pm 0.04$. We also systematically
investigate single-pulse GRBs in the Swift era, finding that only a small
fraction of GRBs (GRBs 120729A, 051111, and 070318) are likely to originate
from an external shock for both the prompt \gamma-ray emission and afterglow.
