The Russian, once ranked two in the world but now 46th, saw off her Czech opponent in 71 minutes to set up a date with 18th seed Jelena Jankovic, who had a first-round bye.
Kuznetsova, who is currently enjoying something of a resurgence after an injury-hampered 2012 season, won 78 per cent of her first service points and was broken just once.
The two-times runner-up at the Indian Wells Tennis Garden had five break opportunities and she took them all in a clinical display to book a clash with Jankovic, who won the tournament in 2010.
"I'm happy to be back on the court, this is the main thing," said Kuznetsova.
"Every day I just try the best I can and things are coming along pretty well. I feel really balanced within myself, which is important."
Kuznetsova was sidelined by a right knee injury for six months last year but has made an encouraging start to the 2013 season, reaching the quarter-finals in Sydney and also at the Australian Open.
In a later match, Italy's Francesca Schiavone downed compatriot Flavia Pennetta 7-5 6-1 to kick off her campaign in winning style.
Schiavone, ranked one place below Kuznetsova, saved eight of 11 break points in an error-strewn first set while breaking Pennetta's serve four times.
The second stanza was more comfortable, although Schiavone still had to save a further three break points on her way to wrapping up victory in an hour and 49 minutes.
Her reward is a tough match-up with second seeded Russian Maria Sharapova.
The top half of the draw gets under way on Thursday, with Britain's Heather Watson and Laura Robson both in action.
Indian Wells results
Christina Mchale (U.S.) beat Tsvetana Pironkova (Bulgaria) 6-3 6-4
Francesca Schiavone (Italy) beat Flavia Pennetta (Italy) 7-5 6-1
Lourdes Dominguez Lino (Spain) beat Grace Min (U.S.) 1-6 6-4 6-3
Maria Sanchez (U.S.) beat Olga Puchkova (Russia) 6-3 6-3
Lesia Tsurenko (Ukraine) beat Ayumi Morita (Japan) 6-1 6-2
Lara Arruabarrena Vecino (Spain) beat Sesil Karatantcheva (Kazakhstan) 6-4 1-6 6-3
Anabel Medina Garrigues (Spain) beat Casey Dellacqua (Australia) 6-1 6-3
Shahar Peer (Israel) beat Marina Erakovic (New Zealand) 6-3 6-4
Svetlana Kuznetsova (Russia) beat Andrea Hlavackova (Czech Republic) 6-3 6-1
Olga Govortsova (Belarus) beat Mandy Minella (Luxembourg) 6-2 3-6 6-4
Mallory Burdette (U.S.) beat Jill Craybas (U.S.) 6-3 6-1
Silvia Soler Espinosa (Spain) beat Vania King (U.S.) 6-7(7) 6-2 6-1
Chanelle Scheepers (South Africa) beat Kristina Mladenovic (France) 6-4 6-1
Johanna Larsson (Sweden) beat Timea Babos (Hungary) 6-7(5) 6-2 6-0
Simona Halep (Romania) beat Lauren Davis (U.S.) 6-2 6-0
Ksenia Pervak (Kazakhstan) beat Zheng Jie (China) 6-1 6-2