Maria Sharapova of Russia (Photo: Reuters)
World number one Williams needed just 65 minutes to deal with fourth seeded defending champion Agnieska Radwanska 6-0 6-3, while Sharapova, who won at Indian Wells earlier this month, demolished Serbia's Jelena Jankovic 6-2 6-1.
Sharapova, extended her winning streak to 11 matches with a lopsided win in just over an hour against Jankovic, a former world number one struggling to regain her best.
Despite Sharapova's good form, Williams will start as clear favourite in Saturday's final - she is 11-2 in meetings with the Russian and has won the last 10 matches between the pair.
Williams, seeking a record sixth Miami title, is relishing the chance of taking on the woman directly below her in the world rankings.
"I love playing her. I love seeing her on the opposite side because she just brings out a good game. I just like the challenge of playing someone who has made history and who is doing so well," the American told reporters.
"She's been playing awesome. I definitely expect a tough match."
One of just 10 women to have won all four grand slams, Sharapova has been collecting titles all over the world but has never won the Sony Open, played in her "home" state of Florida, despite reaching four previous finals.
"It would mean so much to me," she said in a courtside interview. "I love this city. It's the first city I landed in when I came to the United States as a little girl."
In the men's draw, second seed Murray twice fought back from a break down in the first set and then grafted his way through the second to overcome the tall Croat 6-4 6-3.
"It was a tough, tough match. Second set especially was a lot of long, long games and tough points," Murray said.
"I just managed to come through that. Obviously, I took a while to get to the finish line but I thought I played a solid match with not too many errors and was tough in the important moments," the world number three added.
The U.S. Open champion is the highest seed left in the draw after world number one Novak Djokovic lost to 15th seed Tommy Haas and the Briton can leapfrog Roger Federer to second place in the world rankings if he wins the title.
"I'd like to get to number two this week. It would be nice, but I'd rather focus on trying to win my matches," said the Scot, who will fancy his chances against eighth-seeded Gasquet.
Gasquet was solid, hitting 17 winners and breaking serve three times as his 6-3 6-3 victory easily made up for his defeat to the same opponent in the round of 16 at Indian Wells.
The Frenchman knows he will be the underdog against Murray, with the Briton holding a 4-3 head-to-head advantage, but believes he is capable of producing an upset.
"I can win against Andy. He's the favorite, the number three in the world but I know his game, I know how he plays," he said.
Germany's Haas will play Spanish third seed David Ferrer in the other semi-final on Friday.
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