The Australian, currently ranked 35 in the world, needed just 62 minutes to sweep aside the Mexican wildcard 6-1 6-2.
The 29-year-old Tomljanovic, who is in the best form of her career, won 78 per cent of points on serve and never faced a break point despite not sending down a single ace in the humid conditions.
She'll face either 13th-seeded American Madison Keys or Magda Linette of Poland in the round of 32.
Earlier, two-time Australian Open winner Victoria Azarenka and 2019 US Open champion Bianca Andreescu also cruised into round two.
Belarusian Azarenka, who won titles at Melbourne Park in 2012 and 2013, downed Russia's Elina Avanesyan 6-4 6-2 to set up a second-round meeting with Spanish top seed Paula Badosa in a repeat of the Indian Wells final last year.
Canadian Andreescu cruised past Jil Teichmann 6-2 6-4 and set up a first career meeting with Petra Kvitova after the Czech put on a serving masterclass to overpower Bernarda Pera of th US 6-3 7-5.
Russian Liudmila Samsonova, who won in Cleveland and Tokyo this year beat Estonian Kaia Kanepi 6-1 7-5 and China's Zhu Lin defeated Frenchwoman Alize Cornet 3-6 6-3 6-4.
The biggest upset of the day belonged to 20-year-old Colombian Camila Osorio, who broke 15th seed Ekaterina Alexandrova of Russia nine times en route to a 6-4 7-6 (10-8) victory.
American Sloane Stephens, Belgian Elise Mertens, Ukrainian Marta Kostyuk and Canadian Rebecca Marino all advanced after straight sets wins.
Six of the world's top 10 are expected to play in the hard-court tournament, the final 1000-level event this season before the WTA Finals.
Polish world No.1 Iga Swiatek will miss the event after winning in San Diego on Sunday.
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