Nadal, on the quest for his first trophy since October in Tokyo, overpowered Japan's Kei Nishikori 6-4, 6-4 while Wozniacki beat Daniela Hantuchova 6-1, 7-6 (9/7).
World number one Nadal has yet to win a Miami title, finishing runner-up in 2005 to Roger Federer and three years later to Nikolay Davydenko. His win over Nishikori followed one at Wimbledon last year.
"It was one of those first rounds you don't want to see," said the Spaniard. "I'm very happy about how I played today -- I was at a high level tonight.
"The feeling was better than last week, so that's important. The serve worked very well at the end of the match."
World number three Federer notched another match win and another career milestone through a straight-sets win over Radek Stepanek.
The third-seeded Swiss defeated the Czech 6-3, 6-3 to reach the third round.
Seventh seed Tomas Berdych fought past Spain's Ruben Ramirez Hidalgo 6-1, 6-7 (4/7), 6-0.
But there was no joy for Andy Roddick, who became the second Miami title holder in as many years to exit in an opening match.
The American eighth seed, who has been troubled by a low-grade illness for a month, was ambushed by Pablo Cuevas 6-4, 7-6 (7-4).
"I had a little trouble breathing out there today," said Roddick, who will drop from the top 10 in the next rankings.
"I've had something for a little while, but I'm going to have it checked out when I get home.
"I didn't feel good all day. I've had it dating back to Memphis off and on. That's a little too long, I think."
Roddick, who played the Davis Cup tie at the start of the month in Chile, then failed to make the quarter-finals at the Masters 1000 event at Indian Wells.
He was treated on court on Saturday for both his illness and a groin problem.
Cuevas, ranked 67th in the world, had never played Roddick before and made the most of his first chance.
In the third round he will face Frenchman Gilles Simon, who beat German Rainer Schuettler 6-4, 6-3.
Federer, whose 16 grand slam titles are the most in history, joined Pete Sampras on seventh in the all-time win list with 762 career victories. Jimmy Connors sets the pace in that statistic with 1,242.
"It's nice tying Pete, but he could have played for many more years," said Federer. "He could still win some matches on tour now if he wanted to."
"It's a funny stat, but it shows how long I have been around already, how much I've won, all around the world and all the different surfaces. I've played 10, 12 solid seasons, you know," added Federer, who next faces Argentina's Juan Monaco -- a 6-4, 6-7 (2/7), 6-4 winner over Ukrainian Sergiy Stakhovsky.
Germany's Philipp Petzschner upset 10th-seeded Austrian Jurgen Melzer 6-3, 6-4.
French 15th seed Jo-Wilfried Tsonga reached the third round as he beat Russian Teymuraz Gabashvili 6-3, 6-7 (3/7), 6-3, while former top-10 player Mikhail Youzhny crushed Taiwan's Lu Yen-Hsun 6-1, 6-0.
In women's action, fourth seed Samantha Stosur put out Lucie Safarova 6-0, 7-6 (7-1) while sixth seed Jelena Jankovic defeated Klara Zakopalova 7-5, 6-1.
There was also an opening victory for 16th seed Maria Sharapova, a winner over German Sabine Lisicki 6-2, 6-0.
China's Peng Shuai upset 11th seed Svetlana Kuznetsova, hammering the Russian 6-3, 6-1.