Second seed Sharapova fired 27 winners past 28th seed Peng in a 66-minute Philippe Chatrier court demolition. The Russian, a semi-finalist in 2011, and seeking a French Open title to complete a career Grand Slam, has lost just five games in three rounds.
She will next face Czech veteran Klara Zakopalova who put out Russian 22nd seed Anastasia Pavlyuchenkova 6-3, 7-5.
"I came in knowing that I was facing a tough opponent who has beaten me before and against who I have played three sets," said Sharapova. "She can really play, hits the ball really well, so I tried to keep her moving, tried to get her on the run."
Defending champion Li Na, the seventh seed, battled back to defeat America's Christina McHale 3-6, 6-2, 6-1.
The 30-year-old Li had to draw upon her 10-year age gap to prevail over the 36th-ranked American, who had fallen in the first round in 2010 and 2011. "She's a very dangerous player. I was happy I could win the match today because I have more experience," said seventh-seeded Li, who will face Kazakh qualifier Yaroslava Shvedova for a place in the quarter-finals. Italian 14th seed Francesca Schiavone, the 2010 champion and runner-up to Li last year, lost 3-6, 6-3, 8-6 to America's Varvara Lepchenko, the world number 63, who has reached the last 16 of a Grand Slam for the first time.
Schiavone, the oldest player left in the tournament at 31, will lose her place in the world top 20 as a result of her defeat.
Uzbekistan-born Lepchenko, who had defeated 19th seed Jelena Jankovic in the second round, squandered the opportunity to serve for the match in the ninth game of the decider, but held her nerve in the 14th.
It was the 26-year-old's second successive win over Schiavone, having also won in three sets in the second round of the Madrid claycourt tournament in May.
"I was fighting till the end. She played amazing. It's her court. I knew that she's not gonna give it for free. I had to work really hard, and I did," said Lepchenko, who next tackles Petra Kvitova, the fourth-seeded Czech.
Wimbledon champion Kvitova, 22, reached the last 16 for the third time but she did it the hard way, serving up eight double faults and committing 37 unforced errors in her 6-2, 4-6, 6-1 win over Russian world number 109 Nina Bratchikova.
She was only saved by her fierce, flatly hit groundstrokes which left the Portugal-based Bratchikova gasping. "I started well, had a set already, and then I was very aggressive and I knew what I had to do," said Kvitova.
"In the second set I was still like, okay, if I play like the first set, it will be fine. But it wasn't. She played much better than the first set. She had a better serve, and it was tough to return." "She had pressure from the first shot that she played. I was running side to side and that's not my game. So I had to change and be aggressive and put her a little further back." Also making the last 16 was Shvedova, a quarter-finalist in 2010, who eased past Spain's Carla Suarez-Navarro 6-4, 7-5.
Spain's claycourt masters tightened their stranglehold on one half of the French Open draw on Saturday as both David Ferrer and Nicolas Almagro reached the last 16 with straight sets wins. The sixth seeded Ferrer flattened Russia's Mikhail Youzhny 6-0, 6-2, 6-2 in just 101 minutes, whilst Almagro saw off the challenge of Argentina's Leonardo Mayer 6-4, 6-1, 6-2.
With six-times defending champion Rafael Nadal and Marcel Granollers in action later in the day, there was the distinct possibility that half of the qualifiers for the last 16 in the bottom half of the draw could come from Spain. In contrast, there were no Spaniards through into the last 16 in the top half of the draw.
Fourth seed Andy Murray meanwhile made smooth progress into the fourth round and, more importantly, appeared to be injury-free in a 6-3, 6-4, 6-4 demolition of Colombia's Santiago Giraldo. The 30-year-old Ferrer, who has yet to make it past the quarter-finals at Roland Garros despite being one of the best players on clay for the last few years, had Youzhny by the throat from the start, winning the first set 6-0 and leading 2-0 in the second before the Russian got off the mark.
Thereafter Ferrer conceded just another three games as he set up a last 16 round meeting with Granollers or French wild card Paul-Henri Mathieu.
"This match was easier than planned, and I was immediately into the match," he said.
"When the situation was a bit difficult, I managed to overcome these difficulties.
"Like there was a break point, and I managed to get through, thanks to my serve. I managed to dictate the game."
Almagro's routine win over Mayer was his seventh straight victory following his title triumph in Nice last week.
His previous best at Roland Garros were quarter-final appearances in 2008 and 2010 and on both occasions he lost to Nadal who he will face again should the two Spaniards make it through to the last eight.
Nadal, seeking to become the first player to win seven French Open titles, was in action later Saturday against Argentine qualifier Eduardo Schwank.
On his rest day Friday, Murray had been left fielding criticism from such as British legend Virginia Wade and French champion Henri Leconte that he had acted in an unsportsmanlike manner in his win over Jarkko Nieminen on Thursday.
In that tie he had looked down and out in the first few games, clutching at his lower back and legs and needing medical treatment three times.
After dropping the first set 6-1, Murray suddenly settled down in the second and eventually ran out an easy winner.
Many felt his actions could have destabilized his opponent whose game fell apart after the opening set.
Against Giraldo though there was no sign of the back spasms that Murray said had been the problem against Nieminen and a single break in each set was enough to put him through into the last 16 at Roland Garros for the fourth straight year.
"It was very hot so I warmed up very quickly," said Murray.
"I quickly felt better yesterday when I woke up than the day before. I am feeling better than I did, but that's because of all the work my physio has done in the last 48 hours.
"I felt like I moved pretty well. When you are playing Slams you have just got to take each day as it comes - hoping that tomorrow I will feel good again."
Also through to the last 16 was eighth seed Janko Tipsarevic of Serbia who worked his way past Frenchman Julien Benneteau 6-3, 7-5, 6-4.
Tipsarevic won the last five games of the match after being 4-1 down in the third set to reach the last 16 at Roland Garros for the first time and will next take on Almagro.