This work presents two global triplet potential energy surfaces (PESs) for the high-energy reaction N2(X1Σ) + O(3P) → NO(X2Π) + N(4S) - in particular, for the lowest energy 3A′ and 3A″ PESs. In order to obtain the energies needed for fitting analytic surfaces, we carried out multireference configuration interaction (MRCI) calculations based on wave functions obtained from state-averaged complete active space self-consistent field calculations for 2280 geometries for the three lowest 3A″ states and for 2298 geometries for the three lowest 3A′ states. The lowest-energy 3A′ and 3A″ states at each of these geometries were then improved by applying the dynamically scaled external correlation (DSEC) method to all MRCI points, and the resulting DSEC energies were used for construction of the ground-state PES for each symmetry. The many-body component of the DSEC energies for the three-dimensional 3A′ and 3A″ PESs was then least-squares fitted in terms of permutationally invariant polynomials in mixed exponential-Gaussian bond order variables. The global and local minima as well as the transition structures of both the 3A′ and the 3A″ analytic PES were explored. In agreement with previous work, we find that the reverse reaction is barrierless on the 3A″ surface along the minimum energy pathway. However, we have explored several new local minima and transition structures on the 3A′ PES. Furthermore, based on the newly found minima and transition structures, two independent reaction mechanisms have been illustrated for the reaction path on the 3A′ PES. The analytic surfaces may be used for dynamics calculations of electronically adiabatic reactive scattering and energy transfer.