Williams - who counts the French Open, Wimbledon and US Open among the eight titles she has earned in 12 tournaments this year - took just 54 minutes to overwhelm the Israeli, who had zero winners to Williams’ 28.
But Williams also had 28 unforced errors, and her six double faults matched her total of six aces.
While Smashnova clearly had no answer for Williams, the American said she hoped to improve her concentration against quarter-final opponent Jelena Dokic of Yugoslavia.
Dokic closed out unseeded Russian Anastasia Myskina 6-3, 6-4, but needed three match points to do it.
Dokic avenged a loss to Myskina in the semi-finals at Bahia in September, and said she could tell the Russian was nervous.
Myskina had hoped for more in her first appearance in the Championships.
Seventh-seeded Slovakian Daniela Hantuchova also made a first-round exit in her Championships debut, falling 6-2, 7-5 to Bulgarian Magdalena Maleeva.
Hantuchova was a late arrival in Los Angeles after helping Slovakia to their first ever FedCup crown in Spain last weekend.
But Maleeva had little sympathy for any plea of fatigue on the part of her 19-year-old opponent.
In the quarterfinals Maleeva will play Australian Open champion Jennifer Capriati. The third-seeded American defeated Italian Silvia Farina Elia 7-5, 6-1.
The quarter-finals get underway on Friday, when fourth seed Justine Henin meets No. 5 Kim Clijsters in an all-Belgian match, and second-seeded American Venus Williams faces sixth-seeded compatriot Monica Seles.
Results (First round):
Serena Williams (USA) bt Anna Smashnova (Isr) 6-2, 6-2; Jennifer Capriati (USA) bt Silvia Farina Elia (Ita) 7-5, 6-1; Magdalena Maleeva (Bul) bt Daniela Hantuchova (Svk x7) 6-2, 7-5; Jelena Dokic (Yug) bt Anastasia Myskina (Rus) 6-3, 6-4.—AFP