  We compute the generic one-loop contribution involving scalar leptoquarks
(LQ) to the $W$ and $Z$ leptonic decay widths. In our computation we include
for the first time the finite terms and the corrections due to the external
momenta of the electroweak bosons, which is a step beyond the
leading-logarithmic approximation considered in the literature so far. We show
that the terms we include can be numerically quite significant. They amount to
about $20\%$ for scalar LQ masses below $1.5$~TeV, as currently allowed by the
direct searches at the LHC. To further illustrate the relevance of our results
we revisit a model with two light scalar LQs, proposed to accommodate the
$B$-physics anomalies. We show that the finite terms we computed can reduce the
tension with the $Z$-pole data.
