We report the detection of spatially extended CO 1-0 and 5-4 emission in the z=2.49 submillimeter galaxy (SMG) J123707+6214, using the Expanded Very Large Array and the Plateau de Bure Interferometer. The large molecular gas reservoir is spatially resolved into two CO(1-0) components (north-east and south-west; previously identified in CO 3-2 emission) with gas masses of 4.3 and 3.5 x 10^10 (alpha_CO/0.8) Msun. We thus find that the optically invisible north-east component slightly dominates the gas mass in this system. The total molecular gas mass derived from the CO(1-0) observations is ~2.5 times larger than estimated from CO(3-2). The two components are at approximately the same redshift, but separated by ~20 kpc in projection. The morphology is consistent with that of an early-stage merger. The total amount of molecular gas is sufficient to maintain the intense 500 Msun/yr starburst in this system for at least ~160 Myr. We derive line brightness temperature ratios of r_31=0.39+/-0.09 and 0.37+/-0.10, and r_51=0.26+/-0.07 and 0.25+/-0.08 in the two components, respectively, suggesting that the J>=3 lines are substantially subthermally excited. This also suggests comparable conditions for star formation in both components. Given the similar gas masses of both components, this is consistent with the comparable starburst strengths observed in the radio continuum emission. Our findings are consistent with other recent studies that find evidence for lower CO excitation in SMGs than in high-z quasar host galaxies with comparable gas masses. This may provide supporting evidence that both populations correspond to different evolutionary stages in the formation of massive galaxies.