Nadal came from a break down to level the match and made an early break in the third but Murray refused to lie down, taking the Spaniard's serve twice to clinch the set.
Murray wasted chances to break Nadal early in the fourth set and the world number two made two breaks of his own to level the fluctuating night match on Rod Laver Arena.
Nadal broke for a 2-0 lead in the decider; the 20-year-old Spaniard romped through the final set to seal victory in three hours 51 minutes and reach the Australian Open quarter-finals for the first time.
Nadal will play 10th seed Fernando Gonzalez in the last eight.
Images from Day 7 | 6 | 5 | 4 | 3 | 2 | 1
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