We combine results from searches by the CDF and D0 collaborations for a standard model Higgs boson ($H$) in the process $gg\ensuremath{\rightarrow}H\ensuremath{\rightarrow}{W}^{+}{W}^{\ensuremath{-}}$ in $p\overline{p}$ collisions at the Fermilab Tevatron Collider at $\sqrt{s}=1.96\text{ }\text{ }\mathrm{TeV}$. With $4.8\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of integrated luminosity analyzed at CDF and $5.4\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ at D0, the 95% confidence level upper limit on $\ensuremath{\sigma}(gg\ensuremath{\rightarrow}H)\ifmmode\times\else\texttimes\fi{}\mathcal{B}(H\ensuremath{\rightarrow}{W}^{+}{W}^{\ensuremath{-}})$ is 1.75 pb at ${m}_{H}=120\text{ }\text{ }\mathrm{GeV}$, 0.38 pb at ${m}_{H}=165\text{ }\text{ }\mathrm{GeV}$, and 0.83 pb at ${m}_{H}=200\text{ }\text{ }\mathrm{GeV}$. Assuming the presence of a fourth sequential generation of fermions with large masses, we exclude at the 95% confidence level a standard-model-like Higgs boson with a mass between 131 and 204 GeV.