Williams, who turned 33 Monday, was eliminated in the first round of the French Open by Urszula Radwanska; her younger sister Serena went on to win the singles title. Venus Williams hasn't made it as far as the quarterfinals in a grand slam event since she made the U.S. Open semis in 2010.
Nadal broke the men's record for match wins at Roland Garros, where he improved to 59-1, with his lone defeat against Robin Soderling in the fourth round in 2009.
"I want to go out in my peak. That's my goal. But have I peaked yet?" Williams said. "I definitely want to continue my journey to get a few more."
Saturday's victory completed the No. 1-ranked Williams' rebound from a shocking loss to 111th-ranked Virginie Razzano in the first round at Roland Garros a year ago. Since that defeat she's 74-3.
The seven-time champion twice let a lead slip away in the fourth set Friday, then came from behind in the fifth to beat the No. 1-ranked Djokovic 6-4, 3-6, 6-1, 6-7 (3), 9-7.
Williams reached the French Open final for the first time since 2002 when she beat Sara Errani 6-0, 6-1 Thursday. The 15-time Grand Slam champion won her only Roland Garros title 11 years ago, beating sister Venus in the final.
Djokovic, the winner of six major titles, seeks to become the eighth man to complete a career Grand Slam, but he'll have to get past seven-time French Open champion Nadal first.
Williams came from behind in the third set Tuesday and advanced to Roland Garros' final four for the first time since 2003 when she defeated Svetlana Kuznetsova 6-1, 3-6, 6-3.
Federer was eliminated before the semifinals for the second time in past three major events, but only the fifth time in the past nine years at a Grand Slam tournament.
Djokovic will next play 35-year-old Tommy Haas, who became the oldest French Open men's quarterfinalist since 1971 by beating Mikhail Youzhny 6-1, 6-1, 6-3. Haas is also the oldest man to reach the quarters at any major event since Andre Agassi at the 2005 U.S. Open.
The 15-time Grand Slam champion next plays 2009 French Open winner Svetlana Kuznetsova. With a victory, Williams would earn her first berth in a French Open semifinal since 2003.
Mattek-Sands won seven consecutive games to take a 5-0 lead in the final set after the second rain delay of the match. She served out the victory with the sun shining and rain falling, and became the fourth U.S. woman to reach the third round.
Filling a mostly empty stadium court with her familiar shrieks Wednesday, the world's former No. 1 player beat Elena Vesnina of Russia 6-1, 6-4 in a match postponed one day because of rain. That meant Azarenka reached the second round 72 hours after some players.
Djokovic began his bid to win his first French Open title with a 7-6 (5), 6-4, 7-5 victory Tuesday against 58th-ranked David Goffin of Belgium.