We have performed the first direct measurement of two resonances of the $^{7}\mathrm{Be}(\ensuremath{\alpha},\ensuremath{\gamma})^{11}\mathrm{C}$ reaction with unknown strengths using an intense radioactive $^{7}\mathrm{Be}$ beam and the DRAGON recoil separator. We report on the first measurement of the 1155 and 1110 keV resonance strengths of $1.73\ifmmode\pm\else\textpm\fi{}0.25(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.40(\mathrm{syst})\text{ }\text{ }\mathrm{eV}$ and ${125}_{\ensuremath{-}25}^{+27}(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}15(\mathrm{syst})\text{ }\text{ }\mathrm{meV}$, respectively. The present results have reduced the uncertainty in the $^{7}\mathrm{Be}(\ensuremath{\alpha},\ensuremath{\gamma})^{11}\mathrm{C}$ reaction rate to $\ensuremath{\sim}9.4%--10.7%$ over $T=1.5--3\text{ }\text{ }\mathrm{GK}$, which is relevant for nucleosynthesis in the neutrino-driven outflows of core-collapse supernovae ($\ensuremath{\nu}p$ process). We find no effect of the new, constrained reaction rate on $\ensuremath{\nu}p$-process nucleosynthesis.