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The 2004 champion faced an obdurate opponent in Frazier but at nearly half a foot taller, Sharapova's superior power proved to be the difference.
Sharapova broke Frazier's serve and then held off some spirited resistance to take the opener.
And two breaks in the second set were enough for Sharapova to seal the win.
With the match coinciding with England's World Cup quarter-final, the pair played to a noticeably smaller crowd than that which witnessed Andre Agassi's Wimbledon farewell in the previous encounter on Centre Court.
Those who chose to stay away missed an impressive display from fourth seed Sharapova as her usual power from the baseline was interspersed with some delicate touches.
Sharapova's forehand provided her with a stream of winners, despite Frazier's tireless chasing down.
Frazier never let her head drop in desperately difficult conditions - temperatures soared to more than 30C - but ultimately lacked the weapons to hurt Sharapova.
Sharapova said the win had boosted her confidence for the rest of her Wimbledon campaign.
"I got a little bit confused - she'd hit a big serve then follow it up with a double fault. It knocked me out of my rhythm," said Sharapova.
"I had a good workout. She's a pretty solid grass-court player and I had to really work for the match.
"But that definitely makes me feel confident going into the fourth round."
I did not get to watch it, ESPN cut the coverage off before the 1st set ended(way before the match ended). I knew you could do it. Keep on being confident and consistent! 
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