Williams lost to her younger sister, top-seeded Serena, in the championship match in the last four majors. The two had squared off for the title at five of the last six Grand Slams, missing out only at the 2002 Australian Open, when Serena was injured.
The more Serena has tightened her grip on women's tennis, the more Venus - a four-time Grand Slam champion - receded into the pack of challenger.
"It's very disappointing but at this juncture there's nothing I can do about it now," said Venus, who made 86 unforced errors and 12 double faults. "So I have to move on to the next tournament."
The 22-year-old American felt she was not in fighting shape after missing almost a month with a strained abdominal muscle.
"I don't think I had the kind of preparation I wanted and I felt that I had to compensate in other areas," Venus said. "Normally, I could be playing freely and swinging freely and just be completely ready. That made it hard."
Zvonareva is making just her second appearance at Roland Garros. She qualified last year and lost to Serena in the third round.
The 18-year-old is having a breakout season this year, winning her first career title in Bol, Croatia, reaching another semifinal in Strasbourg last week and advancing to six other quarterfinals.
Another Russian recorded an upset Sunday as Nadia Petrova downed seventh seed and 2001 champion Jennifer Capriati of the United States, 6-3, 4-6, 6-3. Capriati has not won a title since the Australian Open in January 2002.
"Of course I'm disappointed," she said. "I've just been working so hard and I thought I had a pretty good chance in this tournament. But it just goes to show, you never know."
Petrova will take on Zvonareva in matchup of Muscovites.
Although the dream final for some is no longer a possibility, an exciting quarterfinal was set up as top-seeded Serena and fifth seed Amelie Mauresmo were winners.
Serema Williams was tested for the first time at the tournament, but overcame No. 16 Ai Sugiyama of Japan, 7-5, 6-3, and Mauresmo routed Spain's Magui Serna, 6-1, 6-2.
Belgians Kim Clijsters and Justin Henin-Hardenne each needed three sets to advance to the quarterfinals. Fourth-seeded Clijsters over came a disastrous start to get past No. 15 Magdalena Maleeva of Bulgaria, 0-6, 6-2, 6-1, and No. 4 Henin-Hardenne beat No. 19 Patty Schnyder of Switzerland.
On the men's side, second seed and Australian Open champion Andre Agassi of the United States dispatched Brazilian Flavio Saretta, 6-2, 6-1, 7-5, to reach the quarterfinals.
Agassi, the 1999 winner, will face the winner of the all-Argentine match between No. 7 Guillermo Coria and Mariano Zabaleta. That match was suspended due to darkness with Coria - one of the hottest players on clay this season - leading, 6-4, 7-6 (7-4), 5-7.
Fourth seed Carlos Moya of Spain topped No. 13 Jiri Novak of the Czech Republic, 7-5, 6-3, 6-2. Moya will meet surprise quarterfinalist Martin Verkerk, who ousted Australian Open runner-up Rainer Schuettler of Germany, 6-3, 6-3, 7-5. By defeating the 11th seed, the hard-serving
Dutchman recorded his best career result in only his third
Three-time champion Gustavo Kuerten of Brazil completed a third-round match that was postponed due to darkness on Saturday when he defeated No. 21 Gaston Gaudio of Argentina, 7-6 (7-1), 7-5, 5-7, 6-3.
Venus Williams claimed the first set in 37 minutes, but Zvonareva refused to lay down and fought back to level the match by taking the second set in 33 minutes.
Venus dropped her serve early in the deciding set but grabbed it straight back. The key break came in the ninth game, which left Zonareva serving for the match. She clinched victory with a solid service game and was able to celebrate her biggest win when Williams sent a backhand wide.
Mauresmo, who was born just 10 miles away from the center of the French capital, in the suburb of St. Germains en Laye, advanced past the fourth round for the first time in nine appearances here.
After dropping just eight games in the previous three rounds, Serena Williams needed 1 hour, 32 minutes to extend her Grand Slam winning streak to 32 matches. She had to rally from 4-2 down to take the first set and gained the crucial break of the second set in the eighth game.
Mauresmo's match began after Williams' had finished and the Frenchwoman had a chance to watch the competition.
"I saw some of her match. She was hesitant and made mistakes," said Mauresmo, who defeated Williams three weeks ago in the semifinals of the Italia Masters in Rome for her first win in their six meetings. "I will seize any opportunity to beat her again."
Clijsters might be feeling confident in her bid for her first career Grand Slam title after winning Rome and reaching
the final at Berlin, but she had trouble establishing her game in the first set against Maleeva.
"I just had no rhythm, I wasn't moving well," Clijsters said. "When you're playing that bad, the only thing you can do is fight until the end. Even with bad tennis, you can still turn those matches around and that's what I did."
Henin-Hardenne celebrated her birthday with her win over Schnyder, but it took her almost two hours in tremendous heat. The Belgian star, who turned 21 on Sunday, took the first set comfortably but dropped her first set of the competition in the second as the conditions took their toll.
Henin-Hardenne felt the tournament's "heat rule" made her eligible for some extra time to recover from the intense humidity, but was told otherwise. She asked for an ice bag in the third set as the temperatures reached the low 90s on court. After cooling down, the former semifinalist broke Schnyder's serve to take a 3-0 lead and cruised to victory.
Eighth-seeded Chanda Rubin of the United States matched her best results here with a 4-6, 6-2, 7-5 win over Hungarian Petra Mandula. She now faces Henin-Hardenne.
No. 24 Conchita Martinez of Spain eliminated sixth seed Lindsay Davenport of the United States. The 2000 finalist took a 6-4, 2-0 lead before Davenport retired with a left foot injury. Martinez will take on Clijsters in the quarterfinals.
Notable deaths of 2014 [PHOTOS]