Agassi and Mauresmo, both seeded fourth, hammered their way into the third round of the opening Grand Slam of the year in sweltering conditions at Melbourne Park.
France's Mauresmo smashed Ludmila Cervanova 6-0, 6-2 before saying that the absence of past champions Serena Williams and Jennifer Capriati meant she feels she could go one better than her runner's-up spot in 1999.
"I feel probably there is an opportunity to take in this tournament...not only because there are some players missing but also because I feel good, because I feel my game is getting better and better," Mauresmo said.
"I've always played some good tennis here," he said.
On Wednesday she played some superb tennis.
Tall with a muscular build, the Frenchwoman overwhelmed 64th-ranked Cervanova in a one-sided match lasting 44 minutes.
"She probably didn't know what to do. I am happy about this one -- we'll just keep going like this and see," Mauresmo said.
Agassi will be hoping he can continue "going like this" after a commanding 6-0, 6-2, 6-4 defeat of Czech qualifier Tomas Berdych.
It took the four-times champion 82 minutes to wrap up his 23rd consecutive win at Melbourne Park, having lifted the title in 2000-01 and 2003. Injury kept him out of the 2002 tournament.
Agassi also won the Open on his first trip to Melbourne Park in 1995 and now rues the nine years at the beginning of his career that he stayed away.
"I wish I had played here every opportunity I had," he said. "Apart from the fact that this place has been so amazing for my career, I just enjoy being here so much."
"I think I didn't play at the time for reasons that were questionable. I was young and I wanted time off," Agassi said.
"I didn't have the respect for the traditions of the game I should have had. I did the same at Wimbledon, those are times you can't have back," he said.
Determined to make up for lost time, Agassi always comes to Melbourne in perfect physical shape, and his performances in his first two matches mark him out once again as a strong favourite.
The tournament's top seeds play later on day three. Andy Roddick faces Bohdan Ulihrach and Justine Henin-Hardenne takes on French qualifier Camille Pin.
