Nava is ranked 203 in the world but the youngster, who knocked out John Millman in the first round, showed he belonged further up the ladder with his confident shot-making, winning the big points to take a gruelling first set in 84 minutes.
Murray struggled with his first serve but is always happy to graft in Grand Slams, and broke the inexperienced Nava twice in the second set to level the match after the American made several unforced errors.
That fuelled Murray as he suddenly found his range on serve, tearing through the third set as Nava failed to sustain his levels from the opener and began to fade, giving the resolute Scot the advantage.
With Nava on the ropes, Murray was ruthless with two early breaks to go 4-0 up. Nava nearly got on the board in the fifth game but Murray stood firm to break again before serving out the set.
"Physically this is the best I've felt in years... I'm getting closer to where I want to be. Hopefully I can have a deep run here," Murray said.
Murray will next meet either 13th seed Matteo Berrettini or Hugo Grenier.
