Nadal, Indian Wells champion in 2007 and 2009, broke pony-tailed Ukrainian Dolgopolov once in the opening set to stamp his authority on the match.
The second seed then broke twice in the second to wrap up a commanding 6-3 6-2 win in one hour, 16 minutes.
"He is a very difficult player to play against," the Spanish left-hander said. "He hits very hard, produces winners from every part of the court. He is a funny player, good for tennis.
"I started very strong and he made a few mistakes, more than usual, with his backhand, which helped me a lot. Being in the quarter-finals here is fantastic for me."
Nadal will next take on
In what was a big shock, Nalbandian recovered from a set down to dump out the sixth seed with two gutsy sets of tennis to set up an encounter with Nadal.