Bookmakers have installed the Frenchwoman, a finalist in Melbourne in 1999, as favourite in an injury-depleted field and she started confidently against Ivanovic to close out the first set in 24 minutes.
However, Mauresmo faltered in the next set as the inexperienced but talented Ivanovic recovered from some early nerves.
Playing in her first Grand Slam event, Ivanovic fought back and broke an occasionally erratic Mauresmo's serve in the third game of the second set for a 2-1 lead.
She dropped her own serve three games later and the pair traded service breaks again in the next two games of an often untidy set.
Ivanovic, the 2004
She drew Mauresmo into longer rallies and hit more clean winners than her more experienced opponent -- 14-11 for the match -- but again appeared to succumb to nerves.
Serving to stay in the match at 5-6, Ivanovic pushed a tentative forehand long on the final point for Mauresmo to break again and close out the match in 67 minutes on Rod Laver Arena centre court at Melbourne Park.
Mauresmo also suffered a scare in the second round when she dropped the first set against Russian teenager Dinara Safina.
She will meet either 21st seed Amy Frazier of the United States or unseeded Russian Evgenia Linetskaya in the next round, with a possible match-up against 2003 winner and seventh seed Serena Williams looming in the quarter-finals.