Safin, the No. 9 seed, fired 22 aces and committed almost half as many unforced errors as Sampras for a grueling 6-2, 6-4, 6-7 (5-7), 7-6 victory.
In beating Sampras for the second time in their last three Grand Slam meetings, the 21-year-old Safin needed just 79 minutes at the outset to open a commanding two-set lead.
Safin will next take on South African Wayne Ferreira, who won an electrifying five-setter over Spain's Albert Costa,4-6, 6-4, 6-4, 6-7 (4-7), 9-7.
Capriati withstood an exhausting 62-minute second set in defeating the 20th seeded Grande, 6-3, 7-6 (11-9) , eventually prevailing on her third match point.
In the quarterfinals, Capriati will take on eighth-seeded Amelie Mauresmo of France, who also had a difficult time of it before ousting Marlene Weingartner of Germany, 6-0, 4-6, 7-5.
Meanwhile, fourth-seeded Kim Clijsters and sixth-seeded Justine Henin won to set up an all-Belgium quarterfinal match. Clijsters needed only 45 minutes to demolish Janette Husarova of Slovakia 6-0, 6-2. Henin notched a 6-0, 6-3 victory over No. 11 Elena Dementieva of Russia.
No. 7 Tommy Haas of Germany, the highest seed remaining on the men's side, downed 11th seed Roger Federer of Switzerland in a thrilling five-set, three and a half hour battle between two of the rising young stars,7-6 (7-3), 4-6, 3-6, 6-4, 8-6.
Haas next goes up against Marcelo Rios of Chile. Rios, the 1998 runnerup here, advanced to his first Grand Slam quarterfinal since 1999 with a 7-5, 6-1, 6-4 triumph over No. 23 seed Nicolas Lapentti of Ecuador.
None of the top six seeds in the men's draw made it past the third round.