The Spaniard needed just one break of serve in each set and saved both of the break points he faced to round out a 6-3 6-4 victory.
After a day of rain and blustery conditions at Crandon Park, Nadal said: "It was difficult to find the right feelings this afternoon, but it's these kind of days where you have to just try to win. That's what I did and I am very happy with that.
"This tournament is a tough tournament and anything can happen. I think I had a good week of practice, so I need to play good in the competition now to try and have success."
Nadal will play the 1,000th match of his career in the third round against Germany's Philipp Kohlschreiber, who beat Taylor Fritz 7-5 3-6 7-6 (7/4).
Second-seed Kei Nishikori encountered few problems on his way to a 6-4 6-3 win over South Africa's Kevin Anderson.
Federico Delbonis caused an upset with a 1-6 7-5 6-2 win over Pablo Carreno Busta, while the third-seeded Milos Raonic made progress with a 6-3 7-5 win over Viktor Troicki.
The Canadian, who pulled out of Indian Wells last week with a hamstring problem, said: "Conditions obviously weren't ideal but I have to be very happy with just the outcome.
"I've put in the work that I can. I have prepared the best I can for this tournament and while I'm not necessarily in the best position right now, fortunately it is a long tournament."
Guido Pella sprang a surprise with a straight-sets victory over ninth seed Grigor Dimitrov.
The world number 158 saved a set point in the second set down 5-4 and again at 6-5, but held on to force a tie-break and, despite double faulting on his first match, point wrapped up a 6-3 7-6 (7/4) win.
Pella will face Nicolas Mahut in the third round after be overcame the number 23 seed Steve Johnson 6-4 5-7 6-4.
The number seven seed Marin Cilic was beaten 6-4 2-6 6-3 by Jeremy Chardy and the 28th-seeded Mischa Zverev is also going home early after a 6-4 6-4 defeat to qualifier Jared Donaldson.
Yoshihito Nishioka was forced to retire with a knee injury when leading 13th seed Jack Sock 4-2 and Jiri Vesely got the better of the 19th-seeded Albert Ramos-Vinolas 7-5 (7/5) 4-6 6-3.
Fernando Verdasco saved five set points in the first set before winning the tie-break and advancing past Ernesto Escobedo with a 7-6 (8/6) 7-5 win.
Donald Young secured a comfortable 6-2 6-4 win over number 11 seed Lucas Pouille and Pablo Cuevas was yet another seed to fall. The 21st seed was beaten 7-5 6-0 by Benoit Paire.
There were also wins for Fabio Fognini, Jan-Lennard Struff, Malek Jaziri and Thomaz Bellucci.
