Making the most of some short early par-fours, and the high altitude, Rahm drove to within a yard of the pin at the 390-yard third hole for a tap-in eagle.
Two more birdies gave Rahm a six-shot lead, before the chasing David Puig marginally reined him in with an eagle at the par-five seventh.
But while Puig faltered with a pair of bogeys down the stretch to end at 15-under par, Rahm completed a bogey-free round to finish the tournament 21-under par.
It was Rahm's second win this season on the LIV tour, after a victory in Hong Kong last month.
Josele Ballester completed an all-Spanish podium, third on 14-under par.
Tyrrell Hatton, who had started the day in second, suffered a double bogey on the second hole and carded four more bogeys in a disappointing final-round 72.
But Rahm and Hatton's team Legion XIII still won by nine strokes, bolstered by their teammate Tom McKibbin's tie for fifth.