We analyse the broad-range shape of the monopole and quadrupole correlation functions of the Baryon Oscillation Spectroscopic Survey Data Release 12 (DR12) CMASS and LOWZ galaxy sample to obtain constraints on the Hubble expansion rate H(z), the angular-diameter distance DA(z), the normalized growth rate f(z)σ8(z) and the physical matter density Ωm h2. We adopt wide and flat priors on all model parameters in order to ensure the results are those of a 'single-probe' galaxy clustering analysis. We also marginalize over three nuisance terms that account for potential observational systematics affecting the measured monopole. However, such Monte Carlo Markov Chain analysis is computationally expensive for advanced theoretical models. We develop a new methodology to speed up the analysis. Using the range 40 h-1 Mpc < s < 180 h-1 Mpc, we obtain {DA(z)rs,fid/rs (Mpc), H(z)rs/rs,fid km s-1 Mpc-1, f(z)σ8(z), Ωm h2} = {956 ± 28, 75.0 ± 4.0, 0.397 ± 0.073, 0.143 ± 0.017} at z = 0.32 and {1421 ± 23, 96.7 ± 2.7, 0.497 ± 0.058, 0.137 ± 0.015} at z = 0.59 where rs is the comoving sound horizon at the drag epoch and rs,fid = 147.66 Mpc for the fiducial cosmology used in this study. Combining our measurements with Planck data, we obtain Ωm = 0.306 ± 0.009, H0 = 67.9 ± 0.7 km s-1 Mpc-1 and σ8 = 0.815 ± 0.009 assuming Λcold dark matter (CDM); Ωk = 0.000 ± 0.003 and w = -1.02 ± 0.08 assuming owCDM. Our results show no tension with the flat ΛCDM cosmological paradigm. This paper is part of a set that analyses the final galaxy clustering data set from Baryon Oscillation Spectroscopic Survey.