Williams broke Karatancheva's serve five times to advance at the clay-court tournament on Sweden's west coast.
Also, third-seeded Klara Zakopalova of the Czech Republic beat Ellen Allgurin of Sweden 6-1, 6-1, Mathilda Johansson of France defeated Julia Cohen of the United States 6-2, 6-3, and Anna Tatishvili of Georgia beat Belinda Bencic of Switzerland 2-6, 6-4, 6-4.
Results from day two of the WTA Swedish Open on Tuesday (x denotes seeding):
First round:
Anna Tatishvili (GEO) bt Belinda Bencic (SUI) 2-6, 6-4, 6-4
Teliana Pereira (BRA) bt Dinah Pfizenmaier (GER) 3-6, 6-2, 7-5
Mathilde Johansson (FRA) bt Julia Cohen (USA) 6-2, 6-3
Alexandra Dulgheru (ROM) bt Caroline Garcia (FRA) 7-6 (7/2), 6-1
Klara Zakopalova (CZE x3) bt Ellen Allgurin (SWE) 6-1, 6-1
Richel Hogenkamp (NED) bt Lara Arruabarrena (ESP) 6-3, 6-3
Lesya Tsurenko (UKR x6) bt Anastasia Grymalska (ITA) 6-3, 5-7, 6-1
Nina Bratchikova (RUS) bt Lesley Kerkhove (NED) 6-3, 6-1
Serena Williams (USA x1) bt Sesil Karatantcheva (KAZ) 6-1, 6-2
Andrea Gmiz (VEN) bt Tsvetana Pironkova (BUL x4) 6-1, 6-3