We studied the molecular gas properties of AzTEC/C159, a star-forming disk galaxy at z = 4:567, in order to better constrain the nature of the high-redshift end of the submillimeter- selected galaxy (SMG) population. We secured 12^CO molecular line detections for the J = 2→1 and J = 5→4 transitions using the Karl G. Jansky Very Large Array (VLA) and the NOrthern Extended Millimeter Array (NOEMA) interferometer. The broad (FWHM ~ 750 km s^-1) and tentative double-peaked profiles of the two 12^CO lines are consistent with an extended molecular gas reservoir, which is distributed in a rotating disk, as previously revealed from [CII] 158 μm line observations. Based on the 12^CO(2→1) emission line, we derived L'_CO = (3.4 ± 0.6)x10^10 Kkm s^-1 pc^2, which yields a molecular gas mass of M_H2 (α_CO/4.3) = (1.5 ± 0.3)x10^11 M_⊙ and unveils a gas-rich system with μ_gas(α_CO/=4.3)≡ M_H2/M_⋆ = 3.3 ± 0.7. The extreme star formation efficiency of AzTEC/C159, parametrized by the ratio L_IR/L'_CO = (216 ± 80) L_⊙ (K km s^-1 pc^2)^-1, is comparable to merger-driven starbursts such as local ultra-luminous infrared galaxies and SMGs. Likewise, the 12^CO(5→4)/CO(2→1) line brightness temperature ratio of r_52 = 0.55 ± 0.15 is consistent with high-excitation conditions as observed in SMGs. Based on mass budget considerations, we constrained the value for the L'_CO – H_2 mass conversion factor in AzTEC/C159, that is, α_CO = 3.9 ^+2.7 _-1.3 M_⊙ K^-1 km^-1 spc^-2, which is consistent with a self-gravitating molecular gas distribution as observed in local star- forming disk galaxies. Cold gas streams from cosmological filaments might be fueling a gravitationally unstable gas-rich disk in AzTEC/C159, which breaks into giant clumps and forms stars as efficiently as in merger-driven systems and generates high gas excitation. These results support the evolutionary connection between AzTEC/C159-like systems and massive quiescent disk galaxies at z ~ 2.