Nadal, who overtook Roger Federer for the No. 1 ranking last August, beat Karanusic 6-2, 6-3, 6-2 in the center-court match Thursday at Rod Laver Arena.
The 22-year-old Spaniard beat Federer in the French Open and Wimbledon finals last year and is the Swiss star's biggest threat to winning a record-equaling 14th Grand Slam singles title.
Nadal, who has dropped only 11 games in six sets in Melbourne, has a 3-0 record against Tommy Haas, his third-round opponent.
Nadal's potential semifinal opponent, fourth-ranked Andy Murray, wasn't seriously challenged in his first real test, ousting 51st-ranked Marcel Granollers of Spain 6-4, 6-2, 6-2 in 1 hour, 50 minutes.
That came after Murray had to be on court only 45 minutes in Tuesday's stifling heat before Andrei Pavel retired with a back injury.
With Scottish flags and tartan hats scattered around Rod Laver Arena on a cool Thursday night, Murray had 37 winners to 18 for Granollers.
"All the work I did is paying off," said Murray, runner-up at the U.S. Open last year. "This is probably the best I've felt coming into a Grand Slam."
Guccione, a giant left-hander, won the opening set in a tiebreak but struggled for the rest of the match once the Frenchman succeeded in
blunting his booming serve.
Simon, seeded sixth for the first Grand Slam of the year, has made huge strides in world tennis over the past 12 months, reaching a career-high ranking of sixth, but has never made it past the third round of a major.
Also Thursday, No. 9 seed James Blake advanced to the third round with a 6-3, 6-2, 6-3 win over French qualifier Sebastien de Chaunac.
In the seventh game of the final set, de Chaunac had a heated discussion with a fan who appeared to be heckling him. Security removed the man from the stadium two games later, with Blake serving for the match.
It was the eighth time in nine attempts that Blake has beaten a qualifier in Grand Slams.
De Chaunac won three matches in qualifying at Melbourne Park to get into the main draw, but his loss Thursday extended his record of never having won consecutive matches in a tour-level event.
While he struggled, four seeded Frenchmen also advanced.
Fifth-seeded Jo-Wilfried Tsonga, last year's runner-up, had a tough 6-7 (4), 7-6 (8), 7-6 (7), 6-2 win over Ivan Ljubicic of Croatia. He joined No. 12 Gael Monfils and No. 24 Richard Gasquet in the third round.
Information from The Associated Press and Reuters was used in this report.