We study the boundary regularity of local weak solutions to nonlinear parabolic systems of the form \(\begin{aligned} \partial _t u^i - \textrm{div} \big ( a(|Du|) Du^i \big )= f^i, \qquad i=1,\dots ,N, \end{aligned}\) in a space-time cylinder \(\Omega _T = \Omega \times (0,T)\) , where \(\Omega \subset \mathbb {R}^n\) ( \(n \ge 2\) ) is a bounded, convex \(C^2\) -domain and \(T>0\) . The inhomogeneity \(f=(f^1,\dots ,f^N)\) belongs to \(L^{n+2+\sigma }(\Omega _T,\mathbb {R}^N)\) for some \(\sigma >0\) . The coefficients \(a:\mathbb {R}_{>0} \rightarrow \mathbb {R}_{>0}\) are of Uhlenbeck-type and satisfy a nonstandard (p, q)-growth condition with \( 2 \le p \le q < p + \frac{4}{n+2}. \) Our main result establishes a local Lipschitz estimate up to the lateral boundary for any local weak solution that vanishes on the lateral boundary of the cylinder.