Hingis, the 1997 Open champion, overwhelmed Russian Alina Jidkova, 6-3, 6-1, while 1994 winner Sanchez-Vicario escaped with a 5-7, 6-4, 7-6 (7-2) victory over Joannette Kruger of South Africa.
Looking for her first Grand Slam tournament win since her triumph in the 1999 Australia Open, Hingis put into practice some new tactics.
Hingis said she was working on being more aggressive, going to the net, stepping into the ball and making things happen instead of lying in wait. ``I think I did that pretty well today,'' the world No. 1 said. ``Especially toward the end.''
Earlier, the feisty Sanchez-Vicario avoided becoming the tournament's first upset victim, delivering an overhand smash to put the finishing touch on a see-saw match marked by 14 service breaks.
``At the end when I needed to, I played well,'' said Sanchez-Vicario, appearing in her 14th U.S. Open. ``But it was a tough match. Always the first one is tough. She played really well.''
``I always fight until the end ... You always have to win the last ball before you beat me.''
RAIN DELAY OFFERS A BREATHER
Competing in her first Grand Slam since getting married after the Wimbledon championships, Sanchez-Vicario may have benefited from a breather she received when rain delayed play for one hour, 45 minutes at the National Tennis Center after Kruger had taken the first set.
Eighth seed Nathalie Tauziat of France also bounced back after the delay, recovering from a 3-6, 2-2 deficit to beat Ludmila Cervanova of Slovakia, ranked 160th in the world, 3-6, 6-2, 6-4.
Advancing with much less labor was 15th-seeded Jennifer Capriati, a 6-4, 6-0 winner against Emmanuelle Gagliardi of Switzerland.
HENMAN INTO SECOND ROUND
The first men's seed to advance was Britain's Tim Henman. The 11th seed claimed a 6-3, 6-3, 6-4 victory in one hour, 45 minutes on Louis Armstrong Stadium court.
The Briton will meet the winner of the first-round match between qualifier Fernando Gonzalez of Chile and American wild card Cecil Mamiit.
Other men's winners in the early going included Germany's Tommy Haas and Frenchman Jerome Golmard. Haas beat Briton Jamie Delgado, 6-3, 6-1, 6-1, while Golmard blasted by Wayne Black of Zimbabwe, 6-2, 6-2, 6-2.
Sanchez-Vicario seemed recharged after the rain break and pulled back to even by breaking Kruger in the 10th game of the second set when a lob landed long.
Kruger, however, took command in the third set with a break that gave her a 5-4 lead and had her serving for the match.
But the feisty Spaniard raced out to triple-breakpoint at 0-40, and broke at 15-40 when Kruger, who made four errors in the critical game, netted a routine forehand.
The tiebreak belonged to Sanchez-Vicario, who ran off five successive points from 2-2, starting with a delicate, running cross-court drop shot that ticked off the net, and ending with her emphatic overhand smash off a weak service return.
EASY ADVANCE FOR CAPRIATI
Capriati, who reached the Open semifinals at the age of 15 in 1991, needed just one hour, six minutes of court time to advance.
Gagliardi, ranked 80th, twisted her right ankle trailing 0-15, 0-5 in the second set and required an injury timeout, but looked to have no answers in any event to the powerful baseline groundstrokes from Capriati.
Four-time Open champion Pete Sampras, seeded fourth this year, was playing the last day match on the featured court against Martin Damm of the Czech Republic.
In night matches, top-seeded Andre Agassi, the 1999 champion, was due to begin defense of his title against fellow-American Alex Kim.
Wimbledon champion Venus Williams was to open the night program at Arthur Ashe Stadium against France's Anne-Gaelle Sidot.