The second seed was given an unexpectedly tough test by Jenkins, who battled well after losing his first service game, but came through it 6-4 7-5 6-4.
Nadal looked frustrated as he was kept on court for two-and-a-half hours by his 18-year-old opponent, but a break in each set proved enough to earn the victory.
"I have played very well this year on hard courts," Nadal said. "I got to the third round in Australia, the final in Miami and I won in Montreal. But I know every match is tough and I know I can lose every match.
"Today was a very difficult match. He played a good match, he has a very good future. Today I needed to play 100% to win.
"I'm very happy I am in the third round. It's my best result here and I hope I can play well in the next match."
Two-time winner Andre Agassi is also through after beating Ivo Karlovic in straight sets. The Croat took Agassi to three tie-breaks but the American finally advanced 7-6 7-6 7-6.
France's Sebastien Grosjean upset 14th seed Thomas Johansson in four sets 6-3 6-2 4-6 6-1, while Spain's Tommy Robredo saw off Brazil's Gustavo Kuerten.
In the women's competition Justine Henin-Hardenne failed to find her best form but still managed to defeat Maria Sanchez Lorenzo in straight sets to reach the third round.
The Belgian, seeded seventh at Flushing Meadow, triumphed in the afternoon sunshine as she saw off her opponent 6-3 6-4.
However, the French Open champion produced a below-par performance against the Spaniard, ranked 99th in the world.
Losing her opening service game was not the start Henin-Hardenne expected, although she managed to battle back from the early disappointment to take the first set.
The second seemed likely to be a cruise for the former US Open champion as some trademark backhand strokes helped her race out to a 4-1 advantage.
Lorenzo managed to get back in the contest before eventually succumbing to defeat in the 10th game of the set.
"I had little ups and downs but a lot of good things," she said. "I have to be more focused in my next match."
Henin-Hardenne will face Cho Yoon-jeong in the next round after the South Korean upset 27th seed Gisela Dulko 6-4 6-3.
There were no such problems for second seed Lindsay Davenport as she needed just 45 minutes to beat Pauline Parmentier.
The American, who won at Flushing Meadows back in 1998, smashed 21 winners in a 6-1 6-1 hammering of the French qualifier.
The world number one's second straight sets victory sets up a third round showdown with Spaniard Anabel Medina Garrigues.
France's Mary Pierce had an easy 6-3 6-2 victory over Katarina Srebotnik of Slovakia, while other seeds safely through include Nathalie Dechy, Tatiana Golovin, Jelena Jankovic and the Russian pair Anastasia Myskina and Elena Likhovtseva.