Williams, who at number 20 in the world is 87 places higher than her 30-year-old opponent, needed just 79 minutes to wrap up a comfortable win in Florianopolis.
The American fired three aces and boasted a first serve points won percentage of 75, compared to Lucic-Baroni’s 59 as she dominated the match throughout.
Williams will next take on Garbine Muguruza, the world number 96 from Spain, in the second round of the event.
Britain's Anne Keothavong was unable to challenge seventh seed Kristina Mlandenovic of France as she suffered a straight sets, 6-3 6-4 defeat.
Keothavong, currently ranked 183 in the world, struggled with the ball in her hand with a first-serve percentage of just 44 leading to her being broken five times.
Defeat for Keothavong further extends a lengthy rough patch and the 29-year-old has now won just one match since last year's Wimbledon.
In Acapulco, top seed Sara Errani began the defence of her title with a regulation 6-3 6-2 win over Alexandra Cadantu of Romania.
Clay-court specialist Errani, who won four titles on the red dirt last year, will meet Eugenie Bouchard in the second round after the Canadian posted a 7-6(5) 6-3 win over Czech Eva Birnerova.
Brasil Cup results
Jana Cepelova (Slovakia) beat 8-Annika Beck (Germany) 7-6(6) 6-4
Olga Puchkova (Russia) beat 3-Kirsten Flipkens (Belgium) 2-6 6-4 6-4
5-Magdalena Rybarikova (Slovakia) beat Kimiko Date-Krumm (Japan) 6-3 6-0
Beatriz Haddad Maia (Brazil) beat Connie Hsu (U.S.) 6-1 6-2
Timea Babos (Hungary) beat Valeria Savinykh (Russia) 7-6(5) 6-7(3) 6-2
1-Venus Williams (U.S.) beat Mirjana Lucic-Baroni (Croatia) 6-3 6-3
Garbine Muguruza Blanco (Spain) beat Kristina Barrois (Germany) 6-2 6-2
7-Kristina Mladenovic (France) beat Anne Keothavong (Britain) 6-3 6-4
Tatjana Malek (Germany) beat Teliana Pereira (Brazil) 6-4 6-2
Acapulco International results
2-Carla Suarez Navarro (Spain) beat Mathilde Johansson (France) 6-1 6-0
Stephanie Foretz Gacon (France) beat Julia Cohen (U.S.) 5-7 7-6(5) 6-0
Karin Knapp (Italy) beat Johanna Larsson (Sweden) 6-3 6-1
3-Alize Cornet (France) beat Catalina Castano (Colombia) 6-1 2-6 6-3
Eugenie Bouchard (Canada) beat Eva Birnerova (Czech Republic) 7-6(5) 6-3
Maria Jose Martinez Sanchez (Spain) beat Alexandra Panova (Russia) 6-3 6-1
Silvia Soler Espinosa (Spain) beat Mandy Minella (Luxembourg) 6-1 7-6(3)
6-Francesca Schiavone (Italy) beat Grace Min (U.S.) 6-4 4-6 6-2
1-Sara Errani (Italy) beat Alexandra Cadantu (Romania) 6-3 6-2
8-Romina Oprandi (Switzerland) beat Alexa Glatch (U.S.) 6-4 2-6 7-5
Maria Teresa Torro (Spain) beat Pauline Parmentier (France) 6-1 6-4