  Back-to-back dijet cross-sections in deeply inelastic scattering (DIS) at
small $x_{\rm Bj}$ are suppressed by many-body multiple scattering and
screening effects arising from gluon saturation at high parton densities. They
are similarly sensitive in these kinematics to large Sudakov logarithms from
soft gluon radiation. Uncovering novel physics in this DIS channel therefore
requires understanding the interplay of the two phenomena. In this work, we
compute the small $x_{\rm Bj}$ inclusive dijet DIS cross-section in
back-to-back kinematics at next-to-leading order (NLO) in the Color Glass
Condensate effective field theory (CGC EFT). Our result includes, for the first
time, all real and virtual NLO contributions to the impact factor. These
include all Sudakov double and single logarithm contributions, as well as all
other finite $\mathcal{O}(\alpha_s)$ terms that contribute at this order. We
demonstrate explicitly that resummations of small $x$ and Sudakov logarithms
can be performed simultaneously in the CGC EFT. This requires that the JIMWLK
kernel for small $x$ evolution of the Weizs\"{a}cker-Williams (WW) gluon
distribution satisfies a kinematic constraint imposed by lifetime ordering of
successive gluon emissions; the corresponding modifications to the kernel,
corresponding to resummations of large double transverse logarithms, are
precisely of the type required to stabilize JIMWLK evolution beyond leading
logarithmic accuracy. We compute the azimuthal harmonics of the NLO
back-to-back distributions and show their sensitivity to both the unpolarized
and linearly polarized WW gluon distributions. Finally, we discuss how TMD
factorization is broken by an emergent saturation scale at small $x$.
