By Martyn Herman
The 24-year-old Russian beat China's Peng Shuai 6-4 6-2 after some initial trouble with her serve on a sweltering Court Two and she is now favorite to repeat her 2004 triumph.
The former world number one cracked her forehand with relentless power against Peng and many of her sizzling winners were greeted with roars of approval by her fiance, towering New Jersey Nets NBA player Sasha Vujacic.
"I was really ready for her to play well today because she has a great game for the grass courts," Sharapova, who had not gone beyond the fourth round since 2006, told reporters.
"She hits the ball hard and flat and fast. So you really have to be ready for each shot.
"I'm doing well. It's only going to get tougher from here. We're in the quarter-final stage of the tournament. Just hope that I raise my level even more."
Peng, queen of the unorthodox with her double-handed forehand and occasional strange, spinny shovel shots, matched Sharapova early on.
Sharapova had to save two break points as the opening two games took nearly 15 minutes and her forehand and serve were both a little hit-or-miss.
Peng threatened again with Sharapova serving at 3-4 but the tall blonde ramped up the volume and the power on her bludgeoning forehand to stay on level terms then broke through in the next game.
Peng, playing in the fourth round of Wimbledon for the first time, panicked, going down 0-40 and although a couple of beefy serves clawed back two of the break points Sharapova pounced on the third when her opponent made a mess of a forehand she was forced to play one-handed.
Clenching her first and shooting determined glances toward her support group, Sharapova was never likely to let her opponent find a way back into the match and the second set had an air of inevitability about it.
(Editing by Ed Osmond)