Sharapova won a nail-biter 6-1 4-6 6-4 against her fellow Russian to set up a clash with Frenchwoman Marion Bartoli.
France's 11th seed Bartoli upset fifth-seeded Czech Petra Kvitova 1-6 6-2 6-0.
Petrova led 2-0 in the third set when rain halted proceedings for an hour and 13 minutes.
Sharapova spoke to her father, Yuri, on the telephone during the break and took his advice to play with increased energy and aggression when play resumed.
Petrova said it was Sharapova's lucky day because she could regroup when the match was slipping away.
"You should ask her what happened," a frustrated Petrova said. "I don't know what went through her head. I had been in control in the third set. I had everything in my hands.
"Maria looked hesitant and she couldn't get a hold of her game. But then after the rain break, actually it went in her favour because she had time to think, regroup, talk to her coach.
"And then she came out completely cool and collected. She started playing big tennis. Unfortunately, luck was on her side today."
Sharapova paused and then shrugged when told of Petrova's remarks.
"Great," Sharapova said. "I'm the winner so whatever she wants to call it is fine with me."
Sharapova was told by her coach, Thomas Hogstedt, during the delay that her father wanted to speak to her.
"I called him," Sharapova said. "I didn't want to hear it after, if I didn't call him. I didn't want to have that conversation.
"He just said, 'Your energy dropped in the beginning of the second set. That's over. That's done. Now you got to go out there and fight.' I wasn't going to leave that court without a fight."
Sharapova's two-hour 14-minute victory was her 11th win in as many three-set matches this year.
"It's a nice statistic," she said. "It certainly wasn't on my mind because every match is different, different circumstances, whether you have started slow and come back in the second set or whether you had a letdown in the second.
"No matter how you start the match, it's always how you finish. Whether it's an hour or whether it's three hours that you're out there, I don't want to give up until the last point.
"That's pretty much the mentality I have."
Sharapova said she was motivated to finish the year strongly after landing the French Open title and an Olympic silver medal.
"I'll tell you, it's a lot tougher mentally, more challenging, to lose a match and say right away, 'I'm hungry for more,'" Sharapova said. "Just because losing is not always fun.
"When you have moments of victory, when you're holding the trophy, you think back to the work you have put in and that's when you realise it's worth it. That's when there is no better motivation.
"If I didn't have that, I would be announcing a retirement, but I'm not. I still have a lot left in me."