Strong gravitational lenses with measured time delays between the multiple images and models of the lens mass distribution allow a one-step determination of the time-delay distance, and thus a measure of cosmological parameters. We present a blind analysis of the gravitational lens RXJ1131-1231 incorporating (1) the newly measured time delays from COSMOGRAIL, the COSmological MOnitoring of GRAvItational Lenses, (2) archival Hubble Space Telescope imaging of the lens system, (3) a new velocity-dispersion measurement of the lens galaxy of 323 ± 20 km s[SUP]-1[/SUP] based on Keck spectroscopy, and (4) a characterization of the line-of-sight structures via observations of the lens' environment and ray tracing through the Millennium Simulation. Our blind analysis is designed to prevent experimenter bias. The joint analysis of the data sets allows a time-delay distance measurement to 6% precision that takes into account all known systematic uncertainties. In combination with the Wilkinson Microwave Anisotropy Probe seven-year (WMAP7) data set in flat wCDM cosmology, our unblinded cosmological constraints for RXJ1131-1231 are H_0=80.0^{+5.8}_{-5.7} km s^{-1} Mpc^{-1}, Ω[SUB]de[/SUB] = 0.79 ± 0.03, and w=-1.25^{+0.17}_{-0.21}. We find the results to be statistically consistent with those from the analysis of the gravitational lens B1608+656, permitting us to combine the inferences from these two lenses. The joint constraints from the two lenses and WMAP7 are H_0=75.2^{+4.4}_{-4.2} km s^{-1} Mpc^{-1}, Ω _de=0.76^{+0.02}_{-0.03}, and w = -1.14^{+0.17}_{-0.20} in flat wCDM, and H_0=73.1^{+2.4}_{-3.6} km s^{-1} Mpc^{-1}, Ω_{Λ}= 0.75^{+0.01}_{-0.02}, and Ω_k=0.003^{+0.005}_{-0.006} in open ΛCDM. Time-delay lenses constrain especially tightly the Hubble constant H [SUB]0[/SUB] (5.7% and 4.0% respectively in wCDM and open ΛCDM) and curvature of the universe. The overall information content is similar to that of Baryon Acoustic Oscillation experiments. Thus, they complement well other cosmological probes, and provide an independent check of unknown systematics. Our measurement of the Hubble constant is completely independent of those based on the local distance ladder method, providing an important consistency check of the standard cosmological model and of general relativity. ; Peer reviewed