The 22-time Grand Slam champion broke the American at the first opportunity in the second game before grabbing the first set in just 28 minutes.
Nadal, who last claimed the title on Madrid's clay in 2017, broke again to take the lead in the second set and kept up the pace, giving a tennis masterclass to Blanch who is still seeking his first tour win.
The age gap between the pair was 21 years and 117 days, the biggest-ever between two opponents at ATP Masters 1000 level.
The American teen committed 27 unforced errors in what was his second ATP tour match after he had made his debut last month in Miami.
"I think today I played against someone with a great future in front of him," Nadal said. "(But) Today he was making mistakes.
"I tried to be there and be solid all the time without taking a lot of risks. I'm happy to be through and I wish him all the very best.
"For me after how things developed the last few years, every time I have a chance to be on court on this amazing stadium with unconditional support means a lot to me. Trying to enjoy every moment."
The win was Nadal's record-extending 57th victory in Madrid, a tournament that he has won five times.
He will play world number 11 De Minaur in the second round on Saturday.
The Australian defeated Nadal 7-5, 6-1 in the second round of the Barcelona Open last week when the Spaniard was playing his first tournament since January.
