In the men's quarter-finals unseeded Spaniard David Ferrer beat 26th seed Dominik Hrbaty 6-2, 6-3 to move through to his first Masters Series semi-final.
Frenchwoman Mauresmo needed just 65 minutes to end the 17-year-old Serbian's giant-killing run in Miami where she had beaten seeded Russians Nadia Petrova and Svetlana Kuznetsova.
"She (Mauresmo) was just playing constantly well," said Belgrade-born Ivanovic, who trains in Switzerland with the same fitness trainer as men's world number one Roger Federer.
"I'm pretty happy with my effort. There are so many things I still have to improve so I'm really looking forward now."
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"I'm focused on that but it's not my main focus," said Mauresmo. "I think the game and also doing well in these big events is more important to me. Of course, I would love to get it (the number one spot) back but my goals are somewhere else."
Russian Maria Sharapova, behind Mauresmo at number three in the rankings, will play Venus Williams in the semi-finals.
The other quarter-final was being played later on Wednesday between Russian Elena Dementieva and Belgian Kim Clijsters.
In the men's draw Ferrer, ranked 44 in the world, will face either his countryman Rafael Nadal or former Australian Open champion Thomas Johansson, who meet later on Wednesday.
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