Invincible on Europe's dusty red clay courts where he has carved out 60 successive victories, Nadal resembled a grasscourt novice at times against 237th-ranked Robert Kendrick but roared back to win 6-7 3-6 7-6 7-5 6-4 on Centre Court.
Agassi, in his 14th and final Wimbledon, had no such trouble against Italy's Andreas Seppi, using all his experience on the slick lawns in a 6-4 7-6 6-4 victory on court one.
Fellow American Andy Roddick, runner-up for the last two years, joined Agassi in the last 32, racing past Florian Mayer 6-4 6-1 6-2, as did Croatian fifth seed Ivan Ljubicic who beat Justin Gimelstob 6-3 7-6 7-5.
Lleyton Hewitt, champion in 2002, was bogged down at two sets all against South Korea's Hyung-Taik Lee when fading light forced the pair off court.
"That was a considerable improvement," said the 36-year-old Agassi, who will bring the curtain down on his glittering career after this year's U.S. Open.
"It's been too long since I've just felt good and been in a place where I could enjoy what's going on out there. Today I was a lot closer to that," Agassi told reporters.
In the women's event, champion Venus Williams was on the verge of defeat to fellow American Lisa Raymond but recovered to win 6-7 7-5 6-2. Top seed Amelie Mauresmo was a comfortable 6-4 6-2 winner over Australia's Samantha Stosur.
While Agassi's progress was untroubled, second seed Nadal's limitations on grass were laid bare as he was given a torrid time by a player competing at only his third grand slam.
The 26-year-old American reeled off six points in a row to snatch the first set tiebreak from 1-4 down and then completely dominated the bemused Mallorcan in the second with his sharp serve and volley game.
Nadalreceived a warning for slow play at the start of the third set but where several claycourters might have been looking for the exit door, he refused to go away.
The double French Open champion sneaked a third-set tiebreak and although he came within two points of defeat in the fourth set he pegged back a tiring Kendrick.
A double fault cost Kendrick his serve at 2-3 in the fifth and a fist-pumping Nadal pounced on his third match point to complete only his second victory from a two-set deficit.
"He was serving unbelievable," said Nadal. "The more matches I play against big servers on this surface, the more I improve."
Williams, who has had an injury-plagued year, also found herself deep in trouble when she trailed Raymond 7-6 5-2.
The sixth seed then unleashed a barrage of winners to take the next eight games on her way to setting up a third-round meeting with Serbia's Jelena Jankovic.
Fourth seed Maria Sharapova, still waiting for a sequel to her 2004 Wimbledon triumph, powered past American Ashley Harkleroad 6-2 6-2.
The 19-year-old Russian was dispatched to court two, graveyard of so many champions over the years, but suffered no alarms.
"You hear a lot more things out there but I think it's good, the fans can get to see you close up and personal," Sharapova told reporters.
A linesman fainted during Nadal's victory as the temperature rose into the high 20s Celsius and several seeds, notably Patty Schynder and Tommy Robredo, got burned.
Schynder became the highest women's casualty so far when the Swiss eighth seed was beaten 4-6 6-1 6-4 by France's Severine Bremond while Spain's Robredo, seeded 11th among the men, fell 7-6 6-2 6-4 to rising Serb teenager Novak Djokovic.
Andy Murray is the last remaining Briton in the singles.
He failed to close out his match with Frenchman Julien Benneteau and will continue the second-round contest on Friday leading two sets to one.