Sharapova, who has not beaten the world number one American since 2004 and has lost 14 consecutive matches in the rivalry, regained her big-match confidence after twice being pushed to three sets by defeating Petra Kvitova 7-5, 6-1.
Top seed Williams pounded German fifth seed Angelique Kerber 6-2, 6-2, taking 62 minutes and ending with seven aces and four breaks of serve in windy conditions.
"When the wind picked up I just had to concentrate," said Williams, who holds six Miami titles. "I felt better today than in any of my other matches.
Fourth seed Sharapova's 90-minute victory over the Kvitova, a fellow Wimbledon champion, was a relief for five-time Miami finalist Sharapova, who had faced huge battle in her previous two victories.
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This time, it was relatively straightforward for the crowd-pleaser as she bids for her first Miami crown.
"I didn't have a good first few games, so I was happy that I was steady, that I kept trying to do the right thing, kept trying to be aggressive," said Sharapova. "It paid off as the match went on, because I made a few too many unforced errors in the beginning.
"She's a grand slam champion," said Sharapova of Kvitova. "You can never underestimate someone that goes on the court that has that experience, that's had such a big win in her career.
"She's capable of playing really great tennis, and I think everyone knows that.