We report the results of a search for νe appearance in a νμ beam in the MINOS long-baseline neutrino experiment. With an improved analysis and an increased exposure of 8.2×1020 protons on the NuMI target at Fermilab, we find that 2sin⁡2(θ23)sin⁡2(2θ13)<0.12(0.20) at 90% confidence level for δ=0 and the normal (inverted) neutrino mass hierarchy, with a best-fit of 2sin⁡2(θ23)sin⁡2(2θ13)=0.041-0.031+0.047(0.079-0.053+0.071). The θ13=0 hypothesis is disfavored by the MINOS data at the 89% confidence level.