The American was forced to save eight break points in the first set against Kournikova before easing away in the second, winning the last eight games of the match to secure victory.
Elsewhere, second seed Justine Henin beat Els Callens 6-1 6-4 in an all-Belgian match. Henin, runner-up to Williams at Wimbledon in 2001, will next face sixth-seeded Bulgarian Magdalena Maleeva who beat American Meilen Tu 6-4 6-3.
First round: Marie-Gaiane Mikaelian (Swi) bt Nathalie Dechy (Fra) 6-4, 3-6, 6-4; Zsofia Gubacsi (Hun) bt Rossana Neffa-De Los Rios (Par) 7-6 (7/3), 3-6, 7-5
Second round: Venus Williams (USA x1) bt Anna Kournikova (Rus) 7-5, 6-0; Justine Henin (Bel x2) bt Els Callens (Bel) 6-1, 6-4; Magdalena Maleeva (Bul x6) bt Meilen Tu (USA) 6-4, 6-3; Eva Dyrberg (Den) bt Anne Kremer (Lux x7) 7-6 (7/5), 7-6 (11/9)
First round: 3-Sebastien Grosjean (France) beat Noam Okun (Israel) 6-4 6-2; Greg Rusedski (Britain) beat 4-Thomas Johansson (Sweden) 6-4 3-6 6-3; 8-Hicham Arazi (Morocco) beat Lionel Roux (France) 7-6 (7-5) 6-2; Marc Gicquel (France) beat Nicolas Mahut (France) 6-4 6-3; Thomas Enqvist (Sweden) beat Francisco Clavet (Spain) 6-3 1-6 6-2; 1-Juan Carlos Ferrero (Spain) beat Michel Kratochvil (Switzerland) 6-3 7-5; 2-Yevgeny Kafelnikov (Russia) beat Max Mirnyi (Belarus) 7-5 7-6 (7-4); Cedric Pioline (France) beat Younes El Aynaoui (Morocco) 6-4 2-1 (El Aynaoui withdrew injured)
Copenhagen Open:
First round: Magnus Larsson (Swe) bt Mikhail Youzhny (Rus) 4-6, 6-3, 6-4; Kenneth Carlsen (Den) bt Wayne Arthurs (Aus) 6-4, 6-4; Cecil Mamiit (USA) bt Anthony Dupuis (Fra) 6-0, 6-3; Davide Sanguinetti (Ita x4) bt Juan Balcells (Spa) 6-7 (1/7), 6-1, 6-2; Neville Goodwin (Rsa) bt Nicolas Kiefer (Ger x3) 6-3, 3-6, 6-4.
Qatar Open
Second round Alicia Molik (Australia) beat Bahia Mouthassine (Morocco) 6-1 6-1; 4-Tamarine Tanasugarn (Thailand) beat Kristie Boogert (Netherlands) 6-2 6-3; Anastasia Myskina (Russia) beat Petra Mandula (Hungary) 6-3 6-0; Maja Matevzic (Slovenia) beat Rachel McQuillan (Australia) 6-3 6-3
First round: Selima Sfar (Tunisia) beat Tina Pisnik (Slovenia) 6-1 6-2; Janette Husarova (Slovakia) beat Angelique Widjaja (Indonesia) 6-4 6-2.—Reuters/AFP