Mauresmo, the Australian Open and Wimbledon champion in 2006, dropped serve only once while breaking Ivanovic five times to advance 6-3, 6-2 to the semifinals.
Ivanovic, the 21-year-old Serb who spent 12 weeks at No. 1 last season while making the Australian Open final and winning the French, frequently followed stinging forehands with unforced errors.
Both had struggled into the quarterfinals, having to save match points in the second round. But while 29-year-old Mauresmo lifted her tempo, Ivanovic's game was erratic.
Fifth-seeded Mauresmo next faces third-seeded and fellow Frenchwoman Marion Bartoli, who beat Italy's Tathiana Garbin 6-3, 6-3.
Mauresmo said she'd improved her serve and worked on other aspects of her game in the off-season with new coach Hugo Lecoq, having overcome the injuries that restricted her the past two years, causing her ranking to slide to No. 23.
"Right from the first tournament some great things are showing,'' she said. "I'm excited because when you work hard and you try things, you want them to work. It's a good start (but) it's just the first week.''
It was her first victory over a Top 10 player since beating Kim Clijsters in the Antwerp final in February 2007 - the last of her 24 career titles.
"It's a long time. I was thinking about it when I came off the court,'' Mauresmo said. "It's showing I'm still there.''
Ivanovic said she didn't have the reserves for another comeback less than 15 hours after saving two match points in the second set of a tough three-setter over Italy's Roberta Vinci on Wednesday night.
"Yesterday, I dug really deep and gained lots of confidence from that,'' she said. "I found it really hard to dig deep again today.
"Lots of times early in the rally I was going for a shot that I wouldn't usually go, taking a little bit more risk, coming to the net a lot. I had so many mis-hits. It was very disappointing.''
But she said it was no setback for her aspirations at the Australian Open, where she lost last year's final to Maria Sharapova.
"I have the potential to,'' win it, she said. "I've worked very hard and I feel very fit.''
Mauresmo converted her first breakpoint chance in the 7th game of the opening set, then held for a 5-3 lead.
She set up two set points with a lob that had Ivanovic leaping and swinging but missing, then wrapped it up when her rival put a forehand long.
She led 3-1 in the second set before Ivanovic broke back, setting up breakpoint with a rifling forehand that just caught the line.
But Mauresmo recovered to win the next four games and skipped into the net to celebrate her sixth win in eight matches against Ivanovic.
It was a cruise for Mauresmo compared with her 5-7, 6-2, 7-6 (11) second-round win over Julie Coin. The 3-hour, 14-minute marathon was her longest match in 13 seasons on tour.
In the other women's quarterfinals, second-seeded Victoria Azarenka of Belarus lost three of her first four service games before recovering for a 7-6 (5), 6-4 win over Lucie Safarova.
The 19-year-old Azarenka will play a semifinal against Italian Sara Errani, who beat Olga Govortsova of Belarus, 6-3, 6-3.
In the men's draw, Spaniard Fernando Verdasco rallied for a 4-6, 6-0, 6-3 win over Florent Serra of France.
Third-seeded Verdasco, linked romantically with Ivanovic, dropped serve in the ninth game to surrender the opening set. But he took the second set in just 26 minutes and, after saving break point at 30-40 in the fifth game of the third with a pinpoint topspin lob, he finished off quickly.
Verdasco, who helped Spain win the Davis Cup final over Argentina, will play Frenchman Paul-Henri Mathieu in the semis.
Mathieu beat 19-year-old Japanese player Kei Nishikori 6-3, 6-4.
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