Henin-Hardenne, hoping to complete a collection of all four Grand Slams by winning Wimbledon, beat French qualifier Severine Bremond 6-4, 6-4.
No. 3 Henin-Hardenne, who hasn't dropped a set in five matches, will play No. 2 Kim Clijsters or Li Na, the first Chinese player to get this far at a Grand Slam.
Sharapova's match was briefly interrupted by a male streaker who got onto the court as she prepared to serve at 3-0 in the second set. She turned her back as the man did a cartwheel and a dance about 10 yards away from her.
Two security guards wrapped a red blanket around the man and led him away. Sharapova showed no reaction, while Dementieva gave a slight smile.
Sharapova beat Dementieva for the fifth time in six career matches. After saving a break point in the first game, she took control, winning seven straight games at one stretch to go up 4-0 in the second set.
Dementieva came back to 4-3 and had a chance to break for 4-4. But she failed to capitalize on two second serves, missing forehand returns both times. Sharapova held and served out the match two games later.
"I got off to a really good start," she said. "I put a lot of pressure on her serve. I played really solid but had a little bit of a letdown in the second set. I had a point for 5-0 on her serve, but played a sloppy point and she gained confidence."
Henin-Hardenne had a tougher-than-expected time before subduing the 26-year-old Bremond, the first qualifier to reach the quarters here since 1999. The 129th-ranked Bremond won three qualifying-round matches and four main-draw matches.
Henin-Hardenne actually fell behind 3-2 in the first set, before breaking back to seize control. She hadn't lost more than three games in a set in her previous matches, but Bremond kept close by taking chances and going to the net.
"She played unbelievable tennis the last two weeks," Henin-Hardenne said. "I was ready to fight but I wasn't feeling very well in the beginning of the match. It took me a while to get a rhythm because she was coming to the net so much."
Henin-Hardenne reached her first Grand Slam final here in 2001, losing to Venus Williams. Since then, she has won the French Open three times and the U.S. Open an Australian Open once each.
"It's great to be back almost at the end of the tournament, and I hope to go to the final one more time," she said.
The men's quarterfinals are set for Wednesday, with three-time defending champion Roger Federer facing the player who last beat him on grass four years and 45 matches ago: Croatia's Mario Ancic.
The winner will face either Sweden's Jonas Bjorkman or Radek Stepanek of the Czech Republic. In the bottom half, the matchups are: 2002 champion Lleyton Hewitt vs. Australian Open runner-up Marcos Baghdatis of Cyprus, and French Open champ Rafael Nadal vs. Finland's Jarkko Nieminen.
Stepanek, Baghdatis, Nadal and Nieminen reached the final eight at Wimbledon for the first time.
Ancic was a qualifier when he beat Federer 6-3, 7-6 (2), 6-3 in the first round of the 2002 championships. The Swiss star has since won seven Grand Slam titles and put himself in line to become one of the best players of all time.
Federer is three wins away from becoming the second player in the Open era to win four straight Wimbledon titles, joining Bjorn Borg (five straight from 1976-80) and Pete Sampras (1997-2000).
Federer is 3-0 against Ancic since the Wimbledon loss, including a 6-4, 6-3, 6-4 win in the quarterfinals of the French Open on clay last month.