  The transverse momentum cross section of $e^+e^-$ pairs in the $Z$-boson mass
region of 66-116 GeV/$c^2$ is precisely measured using Run II data
corresponding to 2.1 fb$^{-1}$ of integrated luminosity recorded by the
Collider Detector at Fermilab. The cross section is compared with quantum
chromodynamic calculations. One is a fixed-order perturbative calculation at
${\cal O}(\alpha_s^2)$, and the other combines perturbative predictions at high
transverse momentum with the gluon resummation formalism at low transverse
momentum. Comparisons of the measurement with calculations show reasonable
agreement. The measurement is of sufficient precision to allow refinements in
the understanding of the transverse momentum distribution.
