<p>The experimentally observed temperature-dependent shear and bulk viscosities of the quark-gluon plasma (QGP), along with its apparent violation of the Kovtun-Son-Starinets (KSS) bound <i>η</i>/<i>s</i> = 1/(4<i>π</i>), necessitate a holographic description that incorporates higher-derivative corrections. We propose a five-dimensional Einstein-Scalar-Maxwell-Gauss-Bonnet model in which a scalar-Gauss-Bonnet coupling <i>H</i>(<i>ϕ</i>) encodes leading curvature corrections. Although no closed-form black hole solution is available, we employ an entropy-production analysis at the event horizon to derive exact analytic formulas for the shear viscosity <i>η</i> and bulk viscosity <i>ζ</i>. These expressions exhibit apparent deviation from the KSS bound and nontrivial temperature dependence. We then perform an independent computation via the retarded Green function (Kubo) method, finding perfect agreement for <i>η</i> and isolating a single constant in <i>ζ</i> that requires numerical determination. Our dual derivation underscores the pivotal role of higher-derivative terms in realistic QGP modeling and demonstrates the efficacy of nonanalytic holographic backgrounds in capturing the dynamics of strongly coupled fluids.</p>