Gonzalez, the world number 11 and Australia 2007 finalist, worked for a heavy win over Evgeny Korolev of Kazakhstan 6-7(5), 6-3, 1-6, 6-3, 6-4.
Seventh-seeded Roddick rained down 29 aces over three and a half hours to defeat Spain's Feliciano Lopez 6-7(4), 6-4, 6-4, 7-6(3).
"It was a long match; I'm just relieved to be through," Roddick said after reaching the fourth round.
The four-time semi-finalist improved to 6-0 over Lopez, winning with 21 unforced errors.
Andy Murray, seeded fifth, reached the fourth round for the third time in four years thanks to a defeat of Frenchman Florent Serra 7-5, 6-1, 6-4.
Women's second seed Dinara Safina satisfied her hunger for victory a day after buying a cookbook on a day off, moving ahead 6-1, 6-2 over Britain's Elena Baltacha.
Second seed Safina said she was only recognised once as she ventured into a Melbourne bookstore, emerging with some light kitchen entertainment to take her mind off the pressure at the first Grand Slam of the season.
"This match was better than medium," she said. "I rate it seven out of 10, but I had some moments when I could do better."
Alona Bondarenko of the Ukraine sent eighth seed Jelena Jankovic to her quickest Melbourne Park loss since 2006 with a 6-2, 6-3 defeat.
The win was a triumph all around for Bondarenko, who had lost nine previous matches against the Serb, winning just one set during that long drought. The winner of this month's title in Tasmania moved into the fourth round of a major for the first time in her career.
Jankovic, who finished the 2008 season at number one, said she was uninspired by her own play.
"It was a tough match overall; for me, it was a big challenge," the Serb said. "It was an uphill battle for me. I made a lot of errors, especially in the beginning.
"I didn't serve well, and my opponent played really well. I didn't raise my level of play and couldn't really find my rhythm in my game."
Belgian comeback queen Justine Henin looked like she had hit the wall early in her struggle with Russian Alisa Kleybanova before rallying for a 3-6, 6-4, 6-2 win in just under two and a half hours.
The former number one and seven-time Grand Slam champion proved her pedigree in the comeback, rallying from a set and 3-1 down.
"I kind of survived a little bit today," Henin said. "It's always good to win this kind of match because I came back from nowhere."
Henin advanced into a match against compatriot Yanina Wickmayer as the US Open semi-finalist also had her share of troubles during her win over Italian Sara Errani 6-1, 6-7(4), 6-3.
Wickmayer was stretched out on her stomach and given pain tablets late in the second set for treatment of back pain in a contest in which she won the opening set easily but had to battle to ensure final victory.