Nadal, who extended his winning streak to 15 matches, pegged Dimitrov back with relentless baseline hitting to take the first set with ease.
But the Bulgarian, who sent down 13 aces in the match, took the fight to the Spaniard in the second set, coming from 3-0 down in a tie-break to level.
Trailing 3-2 in the decider, Dimitrov's forehand crashed into the net to hand Nadal the break he needed. The top seed consolidated to make it 5-2 before serving out the match.
Next up for the 31-year-old is Croatian Marin Cilic, who beat Albert Ramos-Vinolas 6-3 6-4 in another quarter-final.
Roger Federer, the only man who can deny Nadal the year-end world number one ranking, is in action against Frenchman Richard Gasquet later on Friday.
(This version of the story corrects Cilic's age in sixth paragraph to 31 from 30.)
(Reporting by Shrivathsa Sridhar in Bengaluru; editing by Alexander Smith)
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