  We consider for the first time the QED corrections to the evolution of
(un)polarized quark and gluon transverse-momentum-dependent distribution and
fragmentation functions (TMDs in general). By extending their operator
definition to QCD$\times$QED, we provide the mixed new anomalous dimensions up
to ${\cal O}(\alpha_s\alpha)$ and the pure QED ones up to ${\cal O}(\alpha^2)$.
These new corrections are universal for all TMDs up to the flavor of the
considered parton, i.e., the full flavor universality of TMD evolution found in
pure QCD is broken in QCD$\times$QED by the presence of the electric charge. In
addition, we provide the leading-order QED corrections to the matching
coefficients of the unpolarized quark TMD parton distribution function onto its
integrated counterparts at ${\cal O}(\alpha_s^0\alpha)$.
