Seeded only fifth in a tournament he won in 2007 and 2009, Nadal was nevertheless squarely in the spotlight as he played his first hard-court match in 346 days.
After a few tense moments in the opening set, he came through with flying colors, beating 73rd-ranked American Harrison 7-6 (7/3), 6-2 in one hour and 33 minutes.
Nadal was sidelined for seven months recovering from a left knee injury. He returned in February with three clay-court tournaments in Latin America.
The former world No. 1 got his comeback off to a blazing start on clay, with one runner-up finish and two titles.
But he said his knee still wasn't 100 percent, and he wasn't sure if he'd put it to the test on the punishing US hard courts.
"I didn't know if I was going to be able to come here two weeks ago," Nadal said. "I'm very happy to be back here."
Nadal jumped to a 4-1 lead against Harrison, but the American regained a break in the seventh game and went on to level the first set at 4-4.
After two tight games, Nadal was clearly delighted to have saved a break point and hold for a 6-5 lead.
Harrison duly held serve to force the tiebreaker, but his forehand error gave Nadal a 2-1 advantage, which the Spaniard stretched to 4-1 with a service winner followed by a crisp volley winner.
A double fault on his first set point slowed him slightly, but he then sealed the set with a forehand winner.
He broke Harrison twice en route to a 4-1 lead in the second, and this time the American couldn't get back on terms.
Nadal closed it out with a love game, punctuating the victory with an overhead winner.
Nadal moved closer to a projected quarter-final match-up with old foe Roger Federer.
Federer, the defending champion, cruised into the third round with quick 6-2, 6-3 victory over Uzbekistan's Denis Istomin.
"It felt good from the start and I was able to maintain that level of play," said Federer, who didn't face a break point in the 57-minute match. "I never thought he got into the match at all. That gives you even more confidence."
Federer, seeded second behind world No. 1 Novak Djokovic, is seeking a first tournament triumph of 2013 after being denied title repeats at Rotterdam and Dubai.
Federer said he wouldn't be surprised to see Nadal across the net in the quarter-finals.
"Him not having played, for me, doesn't make any difference, really. I still expect him to be really difficult and tough to beat here."
Nadal's fellow Spaniard David Ferrer said much the same, even after he himself became the first major casualty of the tournament.
Ferrer, who has edged ahead of Nadal in the world rankings to No. 4, was beaten 3-6, 6-4, 6-3 by 37th-ranked South African Kevin Anderson.
The defeat followed a comprehensive 6-0, 6-2 loss to Nadal in the final at Acapulco a week earlier.
Perhaps with that rout still in mind, Ferrer said he expected Nadal to flourish on hard courts, just as he has on clay.
"He's playing good," Ferrer said. "He's not playing with pain in his knee and that is a very good point."
Women's top seed and defending champion Victoria Azarenka survived a shaky start to make it safely into the third round with a 6-4, 6-1 victory over two-time former champion Daniela Hantuchova.
Azarenka, unbeaten in 2013 and winner of the Australian Open and the WTA event in Doha, fell behind 4-1 in the first, but surrendered just one game from there.
German fourth seed Angelique Kerber advanced with a 6-3, 6-2 victory over Romanian Irina-Camelia Begu.