The opening set was straightforward for the Spaniard, who broke in the very first game before going on to record a 6-2 success.
World number eight Fish responded with an break of his own in the next set to put himself in the ascendancy. The 29-year-old made that advantage count to seal a 6-3 triumph.
The decisive set saw both players break each other, but it was Nadal who claimed the first match points at 5-4 up. However, Fish held firm to level the match 5-5.
Both then held their next service games as the encounter moved into a winner-takes-all tie-break.
World number two Nadal held his nerve to take the breaker 7-3 and wrap up the victory.