World number two Nadal, playing in his first event since being thrashed by Novak Djokovic in last month's Australian Open final, was always in control during a 6-3, 6-3 victory.
The 17-time Grand Slam champion completed the victory in 1hr 20min at Acapulco's Princess Mundo Imperial venue, defeating his 76th ranked opponent with ease.
The tournament top seed seized the advantage in the opening set, scoring a break to go 3-1 ahead with a delicate lob that left Zverev floundering.
With Nadal's superior variety proving too much for Zverev, the Spaniard quickly wrapped up the opening set.
The second set went with serve until the seventh game, when a wild forehand from Zverev sailed wide to give Nadal the break for a 4-3 lead. Zverev hung his head following the miscue, seemingly realising there was no way back.
Nadal then held for a 5-3 lead and wrapped up victory in the ninth game, moving to match point when Zverev could only plop a return tamely into the net.
Nadal then produced a sublime backhand winner down the line to seal a deserved win.
"I'm happy for the victory. It's never easy against Mischa, especially without competing for a while," said Nadal.
"I'll try to enjoy this moment for the next few hours and then be ready for tomorrow," added Nadal, who said he is wary of the threat posed by the mercurial Kyrgios.
"Nick is one of the most talented players on tour," Nadal said. "It's a big challenge for me and I hope to be ready for it."
Elsewhere Tuesday, Zverev's younger brother Alex had little difficulty in advancing to the second round, defeating Australia's Alexei Popyrin 6-3, 6-3.
Second seed Zverev's service game overwhelmed Popyrin, with the German hammering down 13 aces en route to victory.
Australia's Kyrgios meanwhile was made to work hard for victory in his win over Italy's Andreas Seppi, battling into the second round with a 6-3, 7-5 win.
Third seed John Isner of the United States also had a testing opening game, needing three sets to subdue France's Adrian Mannarino 6-3, 4-6, 6-3.
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